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  • The one-way Fubini property and conditional independence: An equivalence result
    Adv. Math. (IF 1.494) Pub Date : 2020-11-19
    Peter J. Hammond; Yeneng Sun

    A process defined by a continuum of random variables with non-degenerate idiosyncratic risk is not jointly measurable with respect to the usual product σ-algebra. We show that the process is jointly measurable in a one-way Fubini extension of the product space if and only if there is a countably generated σ-algebra given which the random variables are essentially pairwise conditionally independent

    更新日期:2020-11-19
  • Algebraic Calderón-Zygmund theory
    Adv. Math. (IF 1.494) Pub Date : 2020-11-19
    Marius Junge; Tao Mei; Javier Parcet; Runlian Xia

    Calderón-Zygmund theory has been traditionally developed on metric measure spaces satisfying additional regularity properties. In the lack of good metrics, we introduce a new approach for general measure spaces which admit a Markov semigroup satisfying purely algebraic assumptions. We shall construct an abstract form of ‘Markov metric’ governing the Markov process and the naturally associated BMO spaces

    更新日期:2020-11-19
  • Unramified covers and branes on the Hitchin system
    Adv. Math. (IF 1.494) Pub Date : 2020-11-19
    Emilio Franco; Peter B. Gothen; André Oliveira; Ana Peón-Nieto

    We study the locus of the moduli space of GL(n,C)-Higgs bundles on a curve given by those Higgs bundles obtained by pushforward under a connected unramified cover. We equip these loci with a hyperholomorphic bundle so that they can be viewed as BBB-branes, and we introduce corresponding BAA-branes which can be described via Hecke modifications. We then show how these branes are naturally dual via explicit

    更新日期:2020-11-19
  • An approach for weighted mixed-norm estimates for parabolic equations with local and non-local time derivatives
    Adv. Math. (IF 1.494) Pub Date : 2020-11-16
    Hongjie Dong; Doyoon Kim

    We give a unified approach to weighted mixed-norm estimates and solvability for both the usual and time fractional parabolic equations in nondivergence form when coefficients are merely measurable in the time variable. In the spatial variables, the leading coefficients locally have small mean oscillations. Our results extend the previous result in [5] for unmixed Lp-estimates without weights.

    更新日期:2020-11-16
  • Geck's conjecture and the generalized Gelfand-Graev representations in bad characteristic
    Adv. Math. (IF 1.494) Pub Date : 2020-11-16
    Junbin Dong; Gao Yang

    For a connected reductive algebraic group G defined over a finite field Fq, Kawanaka introduced the generalized Gelfand-Graev representations (GGGRs for short) of the finite group G(Fq) in the case where q is a power of a good prime for G. This representation has been widely studied and used in various contexts. Recently, Geck proposed a conjecture, characterizing Lusztig's special unipotent classes

    更新日期:2020-11-16
  • Incongruences for modular forms and applications to partition functions
    Adv. Math. (IF 1.494) Pub Date : 2020-11-16
    Sharon Anne Garthwaite; Marie Jameson

    The study of arithmetic properties of coefficients of modular forms f(τ)=∑a(n)qn has a rich history, including deep results regarding congruences in arithmetic progressions. Recently, work of C.-S. Radu, S. Ahlgren, B. Kim, N. Andersen, and S. Löbrich have employed the q-expansion theory of P. Deligne and M. Rapoport in order to determine more about where these congruences can occur. Here, we apply

    更新日期:2020-11-16
  • D-ultrafilters and their monads
    Adv. Math. (IF 1.494) Pub Date : 2020-11-10
    Jiří Adámek; Lurdes Sousa

    For a number of locally finitely presentable categories K we describe the codensity monad of the full embedding of all finitely presentable objects into K. We introduce the concept of D-ultrafilter on an object, where D is a “nice” cogenerator of K. We prove that the codensity monad assigns to every object an object representing all D-ultrafilters on it. Our result covers e.g. categories of sets, vector

    更新日期:2020-11-12
  • Multifractal analysis of weighted ergodic averages
    Adv. Math. (IF 1.494) Pub Date : 2020-11-09
    Aihua Fan

    We propose to study the multifractal behavior of weighted ergodic averages. Our study in this paper is concentrated on the symbolic dynamics. We introduce a thermodynamic formalism which leads to a multifractal spectrum. It is proved that this thermodynamic formalism applies to different kinds of dynamically defined weights, including stationary ergodic random weights, uniquely ergodic weights etc

    更新日期:2020-11-12
  • A strong form of Plessner's theorem
    Adv. Math. (IF 1.494) Pub Date : 2020-11-09
    Stephen J. Gardiner; Myrto Manolaki

    Let f be a holomorphic, or even meromorphic, function on the unit disc. Plessner's theorem then says that, for almost every boundary point ζ, either (i) f has a finite nontangential limit at ζ, or (ii) the image f(S) of any Stolz angle S at ζ is dense in the complex plane. This paper shows that statement (ii) can be replaced by a much stronger assertion. This new theorem and its analogue for harmonic

    更新日期:2020-11-12
  • On stability of exactness properties under the pro-completion
    Adv. Math. (IF 1.494) Pub Date : 2020-11-09
    Pierre-Alain Jacqmin; Zurab Janelidze

    In this paper we formulate and prove a general theorem of stability of exactness properties under the pro-completion, which unifies several such theorems in the literature and gives many more. The theorem depends on a formal approach to exactness properties proposed in this paper, which is based on the theory of sketches. Our stability theorem has applications in proving theorems that establish links

    更新日期:2020-11-12
  • Affine symmetries and neural network identifiability
    Adv. Math. (IF 1.494) Pub Date : 2020-11-09
    Verner Vlačić; Helmut Bölcskei

    We address the following question of neural network identifiability: Suppose we are given a function f:Rm→Rn and a nonlinearity ρ. Can we specify the architecture, weights, and biases of all feed-forward neural networks with respect to ρ giving rise to f? Existing literature on the subject suggests that the answer should be yes, provided we are only concerned with finding networks that satisfy certain

    更新日期:2020-11-12
  • (G,P)-Opers and global Slodowy slices
    Adv. Math. (IF 1.494) Pub Date : 2020-11-09
    Brian Collier; Andrew Sanders

    In this paper, we introduce a generalization of G-opers for arbitrary parabolic subgroups P

    更新日期:2020-11-12
  • Special irreducible representations of Leavitt path algebras
    Adv. Math. (IF 1.494) Pub Date : 2020-11-09
    P.N. Ánh; T.G. Nam

    Several descriptions of irreducible representations of both Leavitt and hence Cohn path algebras of an arbitrary digraph with coefficients in a commutative field introduced by Chen and Rangaswamy are presented, using both infinite paths on the right and vertices as well as direct limits or factors of cyclic projective ideals of the ordinary quiver algebra. Specific properties of these irreducible representations

    更新日期:2020-11-09
  • Supports of simple modules in cyclotomic Cherednik categories O
    Adv. Math. (IF 1.494) Pub Date : 2020-11-09
    Ivan Losev

    The goal of this paper is to compute the supports of simple modules in the categories O for the rational Cherednik algebras associated to groups G(ℓ,1,n). For this we compute some combinatorial maps on the set of simples: wall-crossing bijections and a certain sl∞-crystal associated to a Heisenberg algebra action on a Fock space.

    更新日期:2020-11-09
  • Spin q–Whittaker polynomials
    Adv. Math. (IF 1.494) Pub Date : 2020-11-06
    Alexei Borodin; Michael Wheeler

    We introduce and study a one-parameter generalization of the q–Whittaker symmetric functions. This is a family of multivariate symmetric polynomials, whose construction may be viewed as an application of the procedure of fusion from integrable lattice models to a vertex model interpretation of a one-parameter generalization of Hall–Littlewood polynomials from [3], [6], [7]. We prove branching and Pieri

    更新日期:2020-11-06
  • Tangle-tree duality in abstract separation systems
    Adv. Math. (IF 1.494) Pub Date : 2020-11-05
    Reinhard Diestel; Sang-il Oum

    We prove a general width duality theorem for combinatorial structures with well-defined notions of cohesion and separation. These might be graphs or matroids, but can be much more general or quite different. The theorem asserts a duality between the existence of high cohesion somewhere local and a global overall tree structure. We describe cohesive substructures in a unified way in the format of tangles:

    更新日期:2020-11-05
  • C2(R2) nonnegative extension by bounded-depth operators
    Adv. Math. (IF 1.494) Pub Date : 2020-08-27
    Fushuai Jiang; Garving K. Luli

    In this paper, we prove the existence of a nonnegative parameter-dependent (nonlinear) C2(R2) extension operator with bounded depth.

    更新日期:2020-11-03
  • Categorical mirror symmetry on cohomology for a complex genus 2 curve
    Adv. Math. (IF 1.494) Pub Date : 2020-08-31
    Catherine Cannizzo

    Motivated by observations in physics, mirror symmetry is the concept that certain manifolds come in pairs X and Y such that the complex geometry on X mirrors the symplectic geometry on Y. It allows one to deduce symplectic information about Y from known complex properties of X. Strominger-Yau-Zaslow [61] described how such pairs arise geometrically as torus fibrations with the same base and related

    更新日期:2020-11-03
  • Harmonic mean curvature flow and geometric inequalities
    Adv. Math. (IF 1.494) Pub Date : 2020-09-09
    Ben Andrews; Yingxiang Hu; Haizhong Li

    We employ the harmonic mean curvature flow of strictly convex closed hypersurfaces in hyperbolic space to prove Alexandrov-Fenchel type inequalities relating quermassintegrals to the total curvature, which is the integral of Gaussian curvature on the hypersurface. The resulting inequality allows us to use the inverse mean curvature flow to prove Alexandrov-Fenchel inequalities between the total curvature

    更新日期:2020-11-03
  • Constructing colimits by gluing vector bundles
    Adv. Math. (IF 1.494) Pub Date : 2020-09-10
    Daniel Schäppi

    As already observed by Gabriel, coherent sheaves on schemes obtained by gluing affine open subsets can be described by a simple gluing construction. An example due to Ferrand shows that this fails in general for pushouts along closed immersions, though the gluing construction still works for flat coherent sheaves. We show that by further restricting this gluing construction to vector bundles, we can

    更新日期:2020-11-03
  • Classification of solutions of an equation related to a conformal log Sobolev inequality
    Adv. Math. (IF 1.494) Pub Date : 2020-09-03
    Rupert L. Frank; Tobias König; Hanli Tang

    We classify all finite energy solutions of an equation which arises as the Euler–Lagrange equation of a conformally invariant logarithmic Sobolev inequality on the sphere due to Beckner. Our proof uses an extension of the method of moving spheres from Rn to Sn and a classification result of Li and Zhu. Along the way we prove a small volume maximum principle and a strong maximum principle for the underlying

    更新日期:2020-11-03
  • Pure pairs. I. Trees and linear anticomplete pairs
    Adv. Math. (IF 1.494) Pub Date : 2020-09-03
    Maria Chudnovsky; Alex Scott; Paul Seymour; Sophie Spirkl

    The Erdős-Hajnal conjecture asserts that for every graph H there is a constant c>0 such that every graph G that does not contain H as an induced subgraph has a clique or stable set of cardinality at least |G|c. In this paper, we prove a conjecture of Liebenau and Pilipczuk [10], that for every forest H there exists c>0, such that every graph G with |G|>1 contains either an induced copy of H, or a vertex

    更新日期:2020-11-03
  • A surface in odd characteristic with discrete and non-finitely generated automorphism group
    Adv. Math. (IF 1.494) Pub Date : 2020-09-16
    Keiji Oguiso

    It was proved by Tien-Cuong Dinh and me that there is a smooth complex projective surface whose automorphism group is discrete and not finitely generated. In this paper, after observing finite generation of the automorphism group of any smooth projective surface birational to any K3 surface over any algebraic closure of the prime field of odd characteristic, we will show that there is a smooth projective

    更新日期:2020-11-03
  • On a uniqueness property of supercuspidal unipotent representations
    Adv. Math. (IF 1.494) Pub Date : 2020-09-10
    Yongqi Feng; Eric Opdam

    The formal degree of a unipotent discrete series character of a simple linear algebraic group over a non-archimedean local field (in the sense of Lusztig [17]), is a rational function of q evaluated at q=q, the cardinality of the residue field. The irreducible factors of this rational function are q and cyclotomic polynomials. We prove that the formal degree of a supercuspidal unipotent representation

    更新日期:2020-11-03
  • 3D quadratic NLS equation with electromagnetic perturbations
    Adv. Math. (IF 1.494) Pub Date : 2020-09-11
    Tristan Léger

    In this paper we study the asymptotic behavior of a quadratic Schrödinger equation with electromagnetic potentials. We prove that small solutions scatter. The proof builds on earlier work of the author for quadratic NLS with a non magnetic potential. The main novelty is the use of various smoothing estimates for the linear Schrödinger flow in place of boundedness of wave operators to deal with the

    更新日期:2020-11-03
  • Asymptotic behavior and stability of mean curvature flow with a conical end
    Adv. Math. (IF 1.494) Pub Date : 2020-09-14
    Siao-Hao Guo

    If the initial hypersurface of an immortal mean curvature flow is asymptotic to a regular cone whose entropy is small, the flow will become asymptotically self-expanding. Moreover, the expander that gives rise to the limiting flow is asymptotically stable as an equilibrium solution of the normalized mean curvature flow.

    更新日期:2020-11-03
  • Analytic torsion for surfaces with cusps II. Regularity, asymptotics and curvature theorem
    Adv. Math. (IF 1.494) Pub Date : 2020-09-11
    Siarhei Finski

    We study the Quillen metric on the determinant line bundle associated with a family of complex singular curves with hyperbolic cusp singularities. More precisely, we fix a family of complex curves, which admit at most double-point singularities. We endow the fibers of this family with Kähler metrics, which are defined away from a finite set of points, a divisor on the total space of the family, in

    更新日期:2020-11-03
  • The Kato square root problem on locally uniform domains
    Adv. Math. (IF 1.494) Pub Date : 2020-10-02
    Sebastian Bechtel; Moritz Egert; Robert Haller-Dintelmann

    We obtain the Kato square root estimate for second order elliptic operators in divergence form with mixed boundary conditions on an open and possibly unbounded set in Rd under two simple geometric conditions: The Dirichlet boundary part is Ahlfors–David regular and a quantitative connectivity property in the spirit of locally uniform domains holds near the Neumann boundary part. This improves upon

    更新日期:2020-11-03
  • On q-series identities for false theta series
    Adv. Math. (IF 1.494) Pub Date : 2020-09-24
    Chris Jennings-Shaffer; Antun Milas

    We prove several infinite families of q-series identities for false theta functions and related series. These identities are motivated by considerations of characters of modules of vertex operator superalgebras and of quantum dilogarithms. We also obtain closely related modular identities of the Göllnitz-Gordon-Andrews type. As a byproduct of our identities, we establish several identities for the

    更新日期:2020-11-03
  • Sign conditions for the existence of at least one positive solution of a sparse polynomial system
    Adv. Math. (IF 1.494) Pub Date : 2020-09-24
    Frédéric Bihan; Alicia Dickenstein; Magalí Giaroli

    We give sign conditions on the support and coefficients of a sparse system of d generalized polynomials in d variables that guarantee the existence of at least one positive real root, based on degree theory and Gale duality. In the case of integer exponents, we relate our sufficient conditions to algebraic conditions that emerged in the study of toric ideals.

    更新日期:2020-11-03
  • On the existence of conic Kähler-Einstein metrics
    Adv. Math. (IF 1.494) Pub Date : 2020-10-02
    Gang Tian; Feng Wang

    In this paper, we prove the conic version of YTD conjecture on log Fano manifolds.

    更新日期:2020-11-03
  • Hadamard products and moments of random vectors
    Adv. Math. (IF 1.494) Pub Date : 2020-09-29
    Rafał Latała; Piotr Nayar

    We derive sharp comparison inequalities between weak and strong moments of random vectors in arbitrary finite dimensional Banach space. As an application, we show that the p-summing constant of any finite dimensional Banach space is upper bounded, up to a universal constant, by the p-summing constant of the Hilbert space of the same dimension. We also apply our result to the concentration of measure

    更新日期:2020-11-03
  • Extracting non-canonical places
    Adv. Math. (IF 1.494) Pub Date : 2020-10-02
    Joaquín Moraga

    Let (X,B) be a log canonical pair and V be a finite set of divisorial valuations with log discrepancy in [0,1). We prove that there exists a projective birational morphism π:Y→X so that the exceptional locus is divisorial, the exceptional divisors are Q-Cartier, and they correspond to elements of V. We study how two such models are related. As applications, we apply the main theorem to the study of

    更新日期:2020-11-03
  • Local curvature estimates of long-time solutions to the Kähler-Ricci flow
    Adv. Math. (IF 1.494) Pub Date : 2020-09-29
    Frederick Tsz-Ho Fong; Yashan Zhang

    We study the local curvature estimates of long-time solutions to the normalized Kähler-Ricci flow on compact Kähler manifolds with semi-ample canonical line bundle. Using these estimates, we prove that on such a manifold, the set of singular fibers of the semi-ample fibration on which the Riemann curvature blows up at time-infinity is independent of the choice of the initial Kähler metric. Moreover

    更新日期:2020-11-03
  • Asymptotic method of moving planes for fractional parabolic equations
    Adv. Math. (IF 1.494) Pub Date : 2020-10-29
    Wenxiong Chen; Pengyan Wang; Yahui Niu; Yunyun Hu

    In this paper, we develop a systematical approach in applying an asymptotic method of moving planes to investigate qualitative properties of positive solutions for fractional parabolic equations. We first obtain a series of needed key ingredients such as narrow region principles, and various asymptotic maximum and strong maximum principles for antisymmetric functions in both bounded and unbounded domains

    更新日期:2020-10-30
  • Type D quiver representation varieties, double Grassmannians, and symmetric varieties
    Adv. Math. (IF 1.494) Pub Date : 2020-10-28
    Ryan Kinser; Jenna Rajchgot

    We unify aspects of the equivariant geometry of type D quiver representation varieties, double Grassmannians, and symmetric varieties GL(a+b)/GL(a)×GL(b); in particular we translate results about singularities of orbit closures, combinatorics of orbit closure containment, and torus equivariant K-theory between these three families. These results are all obtained from our generalization of a construction

    更新日期:2020-10-30
  • SL(n) covariant function-valued valuations
    Adv. Math. (IF 1.494) Pub Date : 2020-10-28
    Jin Li

    Classifications of SL(n) covariant function-valued valuations are established with some assumptions of continuity. New valuations, for example, weighted moment functions, are introduced and our classifications give unified characterizations of the Laplace transform on convex bodies, Lp moment bodies, Lp difference bodies, and polar Lp moment bodies (L−p intersection bodies). Using the new classifications

    更新日期:2020-10-30
  • Finite W-superalgebras via super Yangians
    Adv. Math. (IF 1.494) Pub Date : 2020-10-28
    Yung-Ning Peng

    Let e be an arbitrary even nilpotent element in the general linear Lie superalgebra glM|N and let We be the associated finite W-superalgebra. Let Ym|n be the super Yangian associated to the Lie superalgebra glm|n. A subalgebra of Ym|n, called the shifted super Yangian and denoted by Ym|n(σ), is defined and studied. Moreover, an explicit isomorphism between We and a quotient of Ym|n(σ) is established

    更新日期:2020-10-30
  • The Gray tensor product for 2-quasi-categories
    Adv. Math. (IF 1.494) Pub Date : 2020-10-28
    Yuki Maehara

    We construct an (∞,2)-version of the (lax) Gray tensor product. On the 1-categorical level, this is a binary (or more generally an n-ary) functor on the category of Θ2-sets, and it is shown to be left Quillen with respect to Ara's model structure. Moreover we prove that this tensor product forms part of a “homotopical” (biclosed) monoidal structure, or more precisely a normal lax monoidal structure

    更新日期:2020-10-30
  • Weil–Petersson translation length and manifolds with many fibered fillings
    Adv. Math. (IF 1.494) Pub Date : 2020-10-28
    Christopher Leininger; Yair N. Minsky; Juan Souto; Samuel J. Taylor

    We prove that any mapping torus of a pseudo-Anosov mapping class with bounded normalized Weil–Petersson translation length contains a finite set of transverse and level closed curves with the property that drilling out this set of curves results in one of a finite number of cusped hyperbolic 3–manifolds. Moreover, the set of resulting manifolds depends only on the bound for normalized translation length

    更新日期:2020-10-30
  • Leray's plane steady state solutions are nontrivial
    Adv. Math. (IF 1.494) Pub Date : 2020-10-28
    Mikhail V. Korobkov; Konstantin Pileckas; Remigio Russo

    We study solutions to the obstacle problem for the stationary Navier–Stokes system in a two dimensional exterior domain (flow past a prescribed body). We prove that the classical Leray solution to this problem is always nontrivial. No additional condition (on symmetry or smallness, etc.) is assumed. This is a complete extension of a classical result of C.J. Amick (1988) [1] where nontriviality was

    更新日期:2020-10-30
  • A Larson-Sweedler theorem for Hopf V-categories
    Adv. Math. (IF 1.494) Pub Date : 2020-10-28
    Mitchell Buckley; Timmy Fieremans; Christina Vasilakopoulou; Joost Vercruysse

    The aim of this paper is to extend the classical Larson-Sweedler theorem, namely that a k-bialgebra has a non-singular integral (and in particular is Frobenius) if and only if it is a finite dimensional Hopf algebra, to the ‘many-object’ setting of Hopf categories. To this end, we provide new characterizations of Frobenius V-categories and we develop the integral theory for Hopf V-categories. Our results

    更新日期:2020-10-30
  • Renormalized characteristic forms of the Cheng–Yau metric and global CR invariants
    Adv. Math. (IF 1.494) Pub Date : 2020-10-27
    Taiji Marugame

    For each invariant polynomial Φ, we construct a global CR invariant via the renormalized characteristic form of the Cheng–Yau metric on a strictly pseudoconvex domain. When the degree of Φ is 0, the invariant agrees with the total Q′-curvature. When the degree is equal to the CR dimension, we construct a primed pseudo-hermitian invariant IΦ′ which integrates to the corresponding CR invariant. These

    更新日期:2020-10-30
  • Atomic decomposition of characters and crystals
    Adv. Math. (IF 1.494) Pub Date : 2020-10-27
    Cédric Lecouvey; Cristian Lenart

    Lascoux stated that the type A Kostka-Foulkes polynomials Kλ,μ(t) expand positively in terms of so-called atomic polynomials. For any semisimple Lie algebra, the former polynomial is a t-analogue of the multiplicity of the dominant weight μ in the irreducible representation of highest weight λ. We formulate the atomic decomposition in arbitrary type, and view it as a strengthening of the monotonicity

    更新日期:2020-10-30
  • Non-central sections of the simplex, the cross-polytope and the cube
    Adv. Math. (IF 1.494) Pub Date : 2020-10-26
    Hermann König

    We determine the maximal hyperplane sections of the regular n-simplex, if the distance of the hyperplane to the centroid is fairly large, i.e. larger than the distance of the centroid to the midpoint of edges. Similar results for the n-cube and the l1n-ball were obtained by Moody, Stone, Zach and Zvavitch and by Liu and Tkocz. The maximal hyperplanes in these three cases are perpendicular to the vectors

    更新日期:2020-10-30
  • Global solutions of 3D incompressible MHD system with mixed partial dissipation and magnetic diffusion near an equilibrium
    Adv. Math. (IF 1.494) Pub Date : 2020-10-26
    Jiahong Wu; Yi Zhu

    This paper focuses on the 3D incompressible magnetohydrodynamic (MHD) equations with mixed partial dissipation and magnetic diffusion. Our main result assesses the global stability of perturbations near the steady solution given by a background magnetic field. The stability problem on the MHD equations with partial or no dissipation has attracted considerable interests recently and there are substantial

    更新日期:2020-10-30
  • Ozsváth-Szabó bordered algebras and subquotients of category O
    Adv. Math. (IF 1.494) Pub Date : 2020-10-26
    Aaron D. Lauda; Andrew Manion

    We show that Ozsváth–Szabó's bordered algebra used to efficiently compute knot Floer homology is a graded flat deformation of the regular block of a q-presentable quotient of parabolic category O. We identify the endomorphism algebra of a minimal projective generator for this block with an explicit quotient of the Ozsváth–Szabó algebra using Sartori's diagrammatic formulation of the endomorphism algebra

    更新日期:2020-10-30
  • Smooth and singular maximal averages over 2D hypersurfaces and associated Radon transforms
    Adv. Math. (IF 1.494) Pub Date : 2020-10-26
    Michael Greenblatt

    We prove Lp boundedness results, p>2, for local maximal averaging operators over a smooth 2D hypersurface S with either a C1 density function or a density function with a singularity that grows as |(x,y)|−β for β<2. Suppose one is in coordinates such that the surface is localized near some (x0,y0,z0) at which (0,0,1) is normal to the surface, and suppose the surface is represented as the graph of z0+s(x−x0

    更新日期:2020-10-30
  • Uniqueness of the measure of maximal entropy for geodesic flows on certain manifolds without conjugate points
    Adv. Math. (IF 1.494) Pub Date : 2020-10-26
    Vaughn Climenhaga; Gerhard Knieper; Khadim War

    We prove that for closed surfaces M with Riemannian metrics without conjugate points and genus ≥2 the geodesic flow on the unit tangent bundle T1M has a unique measure of maximal entropy. Furthermore, this measure is fully supported on T1M, is the limiting distribution of closed orbits, and the flow is mixing with respect to this measure. We formulate conditions under which this result extends to higher

    更新日期:2020-10-30
  • On the regularity of Mather's β-function for standard-like twist maps
    Adv. Math. (IF 1.494) Pub Date : 2020-10-26
    Carlo Carminati; Stefano Marmi; David Sauzin; Alfonso Sorrentino

    We consider the minimal average action (Mather's β function) for area preserving twist maps of the annulus. The regularity properties of this function share interesting relations with the dynamics of the system. We prove that the β-function associated to a standard-like twist map admits a unique C1-holomorphic (canonical) complex extension, which coincides with this function on the set of real diophantine

    更新日期:2020-10-30
  • Conserved energies for the one dimensional Gross-Pitaevskii equation
    Adv. Math. (IF 1.494) Pub Date : 2020-10-26
    Herbert Koch; Xian Liao

    We prove the well-posedness results for the one dimensional Gross-Pitaevskii equation in the energy space, which is a complete metric space equipped with a newly introduced metric and with the energy norm describing the Hs regularities of the solutions. We establish a family of conserved energies for the one dimensional Gross-Pitaevskii equation, such that all the energy norms of the solutions are

    更新日期:2020-10-30
  • “Small step” remodeling and counterexamples for weighted estimates with arbitrarily “smooth” weights
    Adv. Math. (IF 1.494) Pub Date : 2020-10-24
    S. Kakaroumpas; S. Treil

    For an Ap weight w the norm of the Hilbert Transform in Lp(w), 1

    更新日期:2020-10-30
  • Riesz transform via heat kernel and harmonic functions on non-compact manifolds
    Adv. Math. (IF 1.494) Pub Date : 2020-10-24
    Renjin Jiang

    Let M be a complete non-compact manifold satisfying the volume doubling condition, with doubling index N and reverse doubling index n, n≤N, both for large balls. Assume a Gaussian upper bound for the heat kernel, and an L2-Poincaré inequality outside a compact set. If 22 on manifolds having at least two Euclidean ends of dimension n. For p∈(max⁡{N,2},∞), the fact that (Rp), (Gp) and (RHp) are equivalent

    更新日期:2020-10-30
  • Strange duality on P2 via quiver representations
    Adv. Math. (IF 1.494) Pub Date : 2020-10-23
    Yao Yuan

    We study Le Potier's strange duality conjecture on P2. We focus on the strange duality map SDcnr,d which involves the moduli space of rank r sheaves with trivial first Chern class and second Chern class n, and the moduli space of 1-dimensional sheaves with determinant OP2(d) and Euler characteristic 0. By using tools in quiver representation theory, we show that SDcnr,d is an isomorphism for r=n or

    更新日期:2020-10-30
  • G(3)-supergeometry and a supersymmetric extension of the Hilbert–Cartan equation
    Adv. Math. (IF 1.494) Pub Date : 2020-10-23
    Boris Kruglikov; Andrea Santi; Dennis The

    We realize the simple Lie superalgebra G(3) as supersymmetry of various geometric structures, most importantly super-versions of the Hilbert–Cartan equation (SHC) and Cartan's involutive PDE system that exhibit G(2) symmetry. We provide the symmetries explicitly and compute, via the first Spencer cohomology groups, the Tanaka–Weisfeiler prolongation of the negatively graded Lie superalgebras associated

    更新日期:2020-10-30
  • Theta operators, refined Delta conjectures, and coinvariants
    Adv. Math. (IF 1.494) Pub Date : 2020-10-20
    Michele D'Adderio; Alessandro Iraci; Anna Vanden Wyngaerd

    We introduce the family of Theta operators Θf indexed by symmetric functions f that allow us to conjecture a compositional refinement of the Delta conjecture of Haglund, Remmel and Wilson [23] for Δen−k−1′en. We show that the 4-variable Catalan theorem of Zabrocki [31] is precisely the Schröder case of our compositional Delta conjecture, and we show how to relate this conjecture to the Dyck path algebra

    更新日期:2020-10-30
  • Quantised Painlevé monodromy manifolds, Sklyanin and Calabi-Yau algebras
    Adv. Math. (IF 1.494) Pub Date : 2020-10-17
    Leonid Chekhov; Marta Mazzocco; Vladimir Rubtsov

    In this paper we study quantum del Pezzo surfaces belonging to a certain class. In particular we introduce the generalised Sklyanin-Painlevé algebra and characterise its PBW/PHS/Koszul properties. This algebra contains as limiting cases the generalised Sklyanin algebra, Etingof-Ginzburg and Etingof-Oblomkov-Rains quantum del Pezzo and the quantum monodromy manifolds of the Painlevé equations.

    更新日期:2020-10-17
  • Künneth formulas for motives and additivity of traces
    Adv. Math. (IF 1.494) Pub Date : 2020-10-17
    Fangzhou Jin; Enlin Yang

    We prove several Künneth formulas in motivic homotopy categories and deduce a Verdier pairing in these categories following SGA5, which leads to the characteristic class of a constructible motive, an invariant closely related to the Euler-Poincaré characteristic. We prove an additivity property of the Verdier pairing using the language of derivators, following the approach of May and Groth-Ponto-Shulman;

    更新日期:2020-10-17
  • Triangulations and soliton graphs for totally positive Grassmannian
    Adv. Math. (IF 1.494) Pub Date : 2020-10-16
    Rachel Karpman; Yuji Kodama

    The KP equation is a nonlinear dispersive wave equation which provides an excellent model for resonant interactions of shallow-water waves. It is well known that regular soliton solutions of the KP equation may be constructed from points in the totally nonnegative Grassmannian Gr(N,M)≥0. Kodama and Williams studied the asymptotic patterns (tropical limit) of KP solitons, called soliton graphs, and

    更新日期:2020-10-17
  • Eisenstein series for rank one unitary groups and some cohomological applications
    Adv. Math. (IF 1.494) Pub Date : 2020-10-16
    Neven Grbac; Joachim Schwermer

    Let U/Q be a unitary group of Q-rank one so that the group of real points U(R)≅U(n,1). The group U is only quasi-split over Q if and only if n=1,2. The cohomology of a congruence subgroup of U is closely related to the theory of automorphic forms. This relation is best captured in the so-called automorphic cohomology spaces H⁎(U,C), a natural module under the action of the group U(Af). This paper gives

    更新日期:2020-10-17
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