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  • Local rigidity of Einstein 4-manifolds satisfying a chiral curvature condition
    Math. Ann. (IF 1.136) Pub Date : 2020-10-14
    Joel Fine, Kirill Krasnov, Michael Singer

    Let (M, g) be a compact oriented Einstein 4-manifold. Write \(R_+\) for the part of the curvature operator of g which acts on self-dual 2-forms. We prove that if \(R_+\) is negative definite then g is locally rigid: any other Einstein metric near to g is isometric to it. This is a chiral generalisation of Koiso’s Theorem, which proves local rigidity of Einstein metrics with negative sectional curvature

    更新日期:2020-10-14
  • An annulus multiplier and applications to the limiting absorption principle for Helmholtz equations with a step potential
    Math. Ann. (IF 1.136) Pub Date : 2020-10-12
    Rainer Mandel, Dominic Scheider

    We consider the Helmholtz equation \(-\Delta u+V \, u - \lambda \, u = f \) on \({\mathbb {R}}^n\) where the potential \(V:{\mathbb {R}}^n\rightarrow {\mathbb {R}}\) is constant on each of the half-spaces \({\mathbb {R}}^{n-1}\times (-\infty ,0)\) and \({\mathbb {R}}^{n-1}\times (0,\infty )\). We prove an \(L^p-L^q\)-Limiting Absorption Principle for frequencies \(\lambda >\max \, V\) with the aid

    更新日期:2020-10-12
  • Niemeier lattices, smooth 4-manifolds and instantons
    Math. Ann. (IF 1.136) Pub Date : 2020-10-08
    Christopher Scaduto

    We show that the set of even positive definite lattices that arise from smooth, simply-connected 4-manifolds bounded by a fixed homology 3-sphere can depend on more than the ranks of the lattices. We provide two homology 3-spheres with distinct sets of such lattices, each containing a distinct nonempty subset of the rank 24 Niemeier lattices.

    更新日期:2020-10-08
  • Boussinesq system with measure forcing
    Math. Ann. (IF 1.136) Pub Date : 2020-10-08
    Piotr B. Mucha, Liutang Xue

    The paper analyzes the Navier–Stokes system coupled with the convective-diffusion equation responsible for thermal effects. It is a version of the Boussinesq approximation with a heat source. The problem is studied in the two dimensional plane and the heat source is a measure transported by the flow. For arbitrarily large initial data, we prove global in time existence of unique regular solutions.

    更新日期:2020-10-08
  • Spectral preorder and perturbations of discrete weighted graphs
    Math. Ann. (IF 1.136) Pub Date : 2020-10-07
    John Stewart Fabila-Carrasco, Fernando Lledó, Olaf Post

    In this article, we introduce a geometric and a spectral preorder relation on the class of weighted graphs with a magnetic potential. The first preorder is expressed through the existence of a graph homomorphism respecting the magnetic potential and fulfilling certain inequalities for the weights. The second preorder refers to the spectrum of the associated Laplacian of the magnetic weighted graph

    更新日期:2020-10-07
  • On the fill-in of nonnegative scalar curvature metrics
    Math. Ann. (IF 1.136) Pub Date : 2020-10-07
    Yuguang Shi, Wenlong Wang, Guodong Wei, Jintian Zhu

    In the first part of this paper, we consider the problem of fill-in of nonnegative scalar curvature (NNSC) metrics for a triple of Bartnik data \((\varSigma ,\gamma ,H)\). We prove that given a metric \(\gamma \) on \({{\mathbf {S}}}^{n-1}\) (\(3\le n\le 7\)), \(({{\mathbf {S}}}^{n-1},\gamma ,H)\) admits no fill-in of NNSC metrics provided the prescribed mean curvature H is large enough (Theorem 4)

    更新日期:2020-10-07
  • On certain subspaces of $${\ell _p}$$ ℓ p for $${0
    Math. Ann. (IF 1.136) Pub Date : 2020-10-01
    Fernando Albiac, José Luis Ansorena, Przemysław Wojtaszczyk

    We construct for each \(0

    更新日期:2020-10-02
  • Diagonal restrictions of p -adic Eisenstein families
    Math. Ann. (IF 1.136) Pub Date : 2020-10-01
    Henri Darmon, Alice Pozzi, Jan Vonk

    We compute the diagonal restriction of the first derivative with respect to the weight of a p-adic family of Hilbert modular Eisenstein series attached to a general (odd) character of the narrow class group of a real quadratic field, and express the Fourier coefficients of its ordinary projection in terms of the values of a distinguished rigid analytic cocycle in the sense of Darmon and Vonk (Duke

    更新日期:2020-10-02
  • Fedosov dg manifolds associated with Lie pairs
    Math. Ann. (IF 1.136) Pub Date : 2020-07-26
    Mathieu Stiénon, Ping Xu

    Given any pair (L, A) of Lie algebroids, we construct a differential graded manifold \((L[1]\oplus L/A,Q)\), which we call Fedosov dg manifold. We prove that the homological vector field Q constructed on \(L[1]\oplus L/A\) by the Fedosov iteration method arises as a byproduct of the Poincaré–Birkhoff–Witt map established in [18]. Finally, using the homological perturbation lemma, we establish a quasi-isomorphism

    更新日期:2020-09-16
  • Vanishing Hessian, wild forms and their border VSP
    Math. Ann. (IF 1.136) Pub Date : 2020-09-14
    Hang Huang, Mateusz Michałek, Emanuele Ventura

    Wild forms are homogeneous polynomials whose smoothable rank is strictly larger than their border rank. The discrepancy between these two ranks is caused by the difference between the limit of spans of a family of zero-dimensional schemes and the span of their flat limit. For concise forms of minimal border rank, we show that the condition of vanishing Hessian is equivalent to being wild. This is proven

    更新日期:2020-09-14
  • Locally constrained curvature flows and geometric inequalities in hyperbolic space
    Math. Ann. (IF 1.136) Pub Date : 2020-09-12
    Yingxiang Hu, Haizhong Li, Yong Wei

    In this paper, we first study the locally constrained curvature flow of hypersurfaces in hyperbolic space, which was introduced by Brendle, Guan and Li (An inverse curvature type hypersurface flow in \({\mathbb {H}}^{n+1}\), preprint). This flow preserves the mth quermassintegral and decreases \((m+1)\)th quermassintegral, so the convergence of the flow yields sharp Alexandrov–Fenchel type inequalities

    更新日期:2020-09-12
  • Globally F-regular type of moduli spaces
    Math. Ann. (IF 1.136) Pub Date : 2020-09-12
    Xiaotao Sun, Mingshuo Zhou

    We prove that moduli spaces of semistable parabolic bundles and generalized parabolic sheaves with fixed determinant on a smooth projective curve are of globally F-regular type.

    更新日期:2020-09-12
  • Energy of sections of the Deligne–Hitchin twistor space
    Math. Ann. (IF 1.136) Pub Date : 2020-09-09
    Florian Beck, Sebastian Heller, Markus Röser

    We study a natural functional on the space of holomorphic sections of the Deligne–Hitchin moduli space of a compact Riemann surface, generalizing the energy of equivariant harmonic maps corresponding to twistor lines. We show that the energy is the residue of the pull-back along the section of a natural meromorphic connection on the hyperholomorphic line bundle recently constructed by Hitchin. As a

    更新日期:2020-09-10
  • Non-archimedean entire curves in closed subvarieties of semi-abelian varieties
    Math. Ann. (IF 1.136) Pub Date : 2020-09-05
    Jackson S. Morrow

    We prove a non-archimedean analogue of the fact that a closed subvariety of a semi-abelian variety is hyperbolic modulo its special locus, and thereby generalize a result of Cherry.

    更新日期:2020-09-06
  • On the cycles of components of disconnected Julia sets
    Math. Ann. (IF 1.136) Pub Date : 2020-09-04
    Guizhen Cui, Wenjuan Peng

    For any integers \(d\ge 3\) and \(n\ge 1\), we construct a hyperbolic rational map of degree d such that it has n cycles of the connected components of its Julia set except single points and Jordan curves.

    更新日期:2020-09-05
  • Multilinear singular integrals on non-commutative $$L^p$$ L p spaces
    Math. Ann. (IF 1.136) Pub Date : 2020-09-04
    Francesco Di Plinio, Kangwei Li, Henri Martikainen, Emil Vuorinen

    We prove \(L^p\) bounds for the extensions of standard multilinear Calderón–Zygmund operators to tuples of \({\text {UMD}}\) spaces tied by a natural product structure. The product can, for instance, mean the pointwise product in \({\text {UMD}}\) function lattices, or the composition of operators in the Schatten-von Neumann subclass of the algebra of bounded operators on a Hilbert space. We do not

    更新日期:2020-09-05
  • Zero relaxation time limits to a hydrodynamic model of two carrier types for semiconductors
    Math. Ann. (IF 1.136) Pub Date : 2020-08-25
    Yan-bo Hu, C. Klingenberg, Yun-guang Lu

    In this paper, we study the zero relaxation time limits to a one dimensional hydrodynamic model of two carrier types for semiconductors. First, we introduce the flux approximation coupled with the classical viscosity method to obtain the uniform \(L_{loc}^{p}, p \ge 1, \) bound of the approximation solutions \( \rho _{i}^{ \varepsilon ,\delta } \) and other estimates of \( (u_{i}^{ \varepsilon ,\delta

    更新日期:2020-08-25
  • Central values of L -functions of cubic twists
    Math. Ann. (IF 1.136) Pub Date : 2020-08-25
    Eugenia Rosu

    We are interested in finding for which positive integers D we have rational solutions for the equation \(x^3+y^3=D.\) The aim of this paper is to compute the value of the L-function \(L(E_D, 1)\) for the elliptic curves \(E_D: x^3+y^3=D\). For the case of p prime \(p\equiv 1\mod 9\), two formulas have been computed by Rodriguez-Villegas and Zagier. We have computed formulas that relate \(L(E_D, 1)\)

    更新日期:2020-08-25
  • Correction to: Poles and residues of standard L -functions attached to Siegel modular forms
    Math. Ann. (IF 1.136) Pub Date : 2020-08-18
    Shin-ichiro Mizumoto

    Correction to my paper on the poles of standard L-functions attached to Siegel modular forms.

    更新日期:2020-08-18
  • Homotopical and operator algebraic twisted K -theory
    Math. Ann. (IF 1.136) Pub Date : 2020-08-15
    Fabian Hebestreit, Steffen Sagave

    Using the framework for multiplicative parametrized homotopy theory introduced in joint work with C. Schlichtkrull, we produce a multiplicative comparison between the homotopical and operator algebraic constructions of twisted K-theory, both in the real and complex case. We also improve several comparison results about twisted K-theory of \(C^*\)-algebras to include multiplicative structures. Our results

    更新日期:2020-08-15
  • The fibration method over real function fields
    Math. Ann. (IF 1.136) Pub Date : 2020-08-15
    Ambrus Pál, Endre Szabó

    Let \(\mathbb R(C)\) be the function field of a smooth, irreducible projective curve over \(\mathbb R\). Let X be a smooth, projective, geometrically irreducible variety equipped with a dominant morphism f onto a smooth projective rational variety with a smooth generic fibre over \(\mathbb R(C)\). Assume that the cohomological obstruction introduced by Colliot-Thélène is the only one to the local-global

    更新日期:2020-08-15
  • Weil–Petersson Teichmüller space III: dependence of Riemann mappings for Weil–Petersson curves
    Math. Ann. (IF 1.136) Pub Date : 2020-08-14
    Yuliang Shen, Li Wu

    The classical Riemann mapping theorem implies that there exists a so-called Riemann mapping which takes the upper half plane onto the left domain bounded by a Jordan curve in the extended complex plane. The primary purpose of the paper is to study the basic problem: how does a Riemann mapping depend on the corresponding Jordan curve? We are mainly concerned with those Jordan curves in the Weil–Petersson

    更新日期:2020-08-14
  • On the Gibbons’ conjecture for equations involving the p -Laplacian
    Math. Ann. (IF 1.136) Pub Date : 2020-08-13
    Francesco Esposito, Alberto Farina, Luigi Montoro, Berardino Sciunzi

    In this paper we prove the validity of Gibbons’ conjecture for the quasilinear elliptic equation \( -\Delta _p u = f(u) \) on \(\mathbb {R}^N.\) The result holds true for \((2N+2)/(N+2)< p < 2\) and for a very general class of nonlinearity f.

    更新日期:2020-08-14
  • Topological full groups and t.d.l.c. completions of Thompson’s V
    Math. Ann. (IF 1.136) Pub Date : 2020-08-12
    Waltraud Lederle

    We show that every topological full group coming from a one-sided irreducible shift of finite type, in the sense of Matui, is isomorphic to a group of tree almost automorphisms preserving an edge colouring of the tree. As an application, we prove that it admits totally disconnected, locally compact completions of arbitrary nonempty finite local prime content. The completions we construct have open

    更新日期:2020-08-12
  • Multiplicity sequence and integral dependence
    Math. Ann. (IF 1.136) Pub Date : 2020-08-12
    Claudia Polini, Ngo Viet Trung, Bernd Ulrich, Javid Validashti

    We prove that two arbitrary ideals \(I \subset J\) in an equidimensional and universally catenary Noetherian local ring have the same integral closure if and only if they have the same multiplicity sequence. We also obtain a Principle of Specialization of Integral Dependence, which gives a condition for integral dependence in terms of the constancy of the multiplicity sequence in families.

    更新日期:2020-08-12
  • Character rigidity of simple algebraic groups
    Math. Ann. (IF 1.136) Pub Date : 2020-08-12
    Bachir Bekka

    We prove the following extension of Tits’ simplicity theorem. Let \(k\) be an infinite field, G an algebraic group defined and quasi-simple over \(k,\) and \(G(k)\) the group of \(k\)-rational points of G. Let \(G(k)^+\) be the subgroup of \(G(k)\) generated by the unipotent radicals of parabolic subgroups of G defined over \(k\) and denote by \(PG(k)^+\) the quotient of \(G(k)^+\) by its center. Then

    更新日期:2020-08-12
  • Height gap conjectures, D -finiteness, and a weak dynamical Mordell–Lang conjecture
    Math. Ann. (IF 1.136) Pub Date : 2020-08-12
    Jason P. Bell, Fei Hu, Matthew Satriano

    In previous work, the first author, Ghioca, and the third author introduced a broad dynamical framework giving rise to many classical sequences from number theory and algebraic combinatorics. Specifically, these are sequences of the form \(f(\Phi ^n(x))\), where \(\Phi :X\dasharrow X\) and \(f:X\dasharrow {\mathbb {P}}^1\) are rational maps defined over \(\overline{{\mathbb {Q}}}\) and \(x\in X(\overline{{\mathbb

    更新日期:2020-08-12
  • Rigidity results for von Neumann algebras arising from mixing extensions of profinite actions of groups on probability spaces
    Math. Ann. (IF 1.136) Pub Date : 2020-08-11
    Ionut Chifan, Sayan Das

    Motivated by Popa’s seminal work Popa (Invent Math 165:409-45, 2006), in this paper, we provide a fairly large class of examples of group actions \(\Gamma \curvearrowright X\) satisfying the extended Neshveyev–Størmer rigidity phenomenon Neshveyev and Størmer (J Funct Anal 195(2):239-261, 2002): whenever \(\Lambda \curvearrowright Y\) is a free ergodic pmp action and there is a \(*\)-isomorphism \(\Theta

    更新日期:2020-08-11
  • The squeezing function on doubly-connected domains via the Loewner differential equation
    Math. Ann. (IF 1.136) Pub Date : 2020-08-11
    Tuen Wai Ng, Chiu Chak Tang, Jonathan Tsai

    For any bounded domains \(\varOmega \) in \({\mathbb {C}}^{n}\), Deng, Guan and Zhang introduced the squeezing function \(S_\varOmega (z)\) which is a biholomorphic invariant of bounded domains. We show that for \(n=1\), the squeezing function on an annulus \(A_r = \lbrace z \in {\mathbb {C}} : r<|z| <1 \rbrace \) is given by \(S_{A_r}(z)= \max \left\{ |z| ,\frac{r}{|z|} \right\} \) for all \(0

    更新日期:2020-08-11
  • An optimal insulation problem
    Math. Ann. (IF 1.136) Pub Date : 2020-08-11
    Francesco Della Pietra, Carlo Nitsch, Cristina Trombetti

    In this paper we consider a minimization problem which arises from thermal insulation. A compact connected set K, which represents a conductor of constant temperature, say 1, is thermally insulated by surrounding it with a layer of thermal insulator, the open set \(\Omega {\setminus } K\) with \(K\subset \bar{\Omega }\). The heat dispersion is then obtained as $$\begin{aligned} \inf \left\{ \int _{\Omega

    更新日期:2020-08-11
  • Periodic Maxwell–Chern–Simons vortices with concentrating property
    Math. Ann. (IF 1.136) Pub Date : 2020-08-09
    Weiwei Ao, Ohsang Kwon, Youngae Lee

    In order to study electrically and magnetically charged vortices in fractional quantum Hall effect and anyonic superconductivity, the Maxwell–Chern–Simons (MCS) model was introduced by Lee et al. (Phys Lett B 252:79–83, 1990) as a unified system of the classical Abelian–Higgs model (AH) and the Chern–Simons (CS) model. In this article, the first goal is to obtain the uniform (CS) limit result of (MCS)

    更新日期:2020-08-09
  • Asymptotic trace formula for the Hecke operators
    Math. Ann. (IF 1.136) Pub Date : 2020-08-08
    Junehyuk Jung, Naser Talebizadeh Sardari

    Given integers m, n and k, we give an explicit formula with an optimal error term (with square root cancelation) for the Petersson trace formula involving the mth and nth Fourier coefficients of an orthonormal basis of \(S_k\left( N\right) ^*\) (the weight k newforms with fixed square-free level N) provided that \(|4 \pi \sqrt{mn}- k|=o\left( k^{\frac{1}{3}}\right) \). Moreover, we establish an explicit

    更新日期:2020-08-08
  • The bilinear Hilbert transform in UMD spaces
    Math. Ann. (IF 1.136) Pub Date : 2020-08-05
    Alex Amenta, Gennady Uraltsev

    We prove \(L^p\)-bounds for the bilinear Hilbert transform acting on functions valued in intermediate UMD spaces. Such bounds were previously unknown for UMD spaces that are not Banach lattices. Our proof relies on bounds on embeddings from Bochner spaces \(L^p(\mathbb {R};X)\) into outer Lebesgue spaces on the time-frequency-scale space \(\mathbb {R}^3_+\).

    更新日期:2020-08-05
  • Gelfand pairs admit an Iwasawa decomposition
    Math. Ann. (IF 1.136) Pub Date : 2020-08-03
    Nicolas Monod

    Every Gelfand pair (G, K) admits a decomposition \(G=KP\), where \(P

    更新日期:2020-08-03
  • Ancient solutions to mean curvature flow for isoparametric submanifolds
    Math. Ann. (IF 1.136) Pub Date : 2020-08-03
    Xiaobo Liu, Chuu-Lian Terng

    Mean curvature flow for isoparametric submanifolds in Euclidean spaces and spheres was studied in Liu and Terng (Duke Math J 147(1):157–179, 2009). In this paper, we will show that all these solutions are ancient solutions and study their limits as time goes to negative infinity. We also discuss rigidity of ancient mean curvature flows for hypersurfaces in spheres and its relation to the Chern’s conjecture

    更新日期:2020-08-03
  • New estimates of the maximal Bochner–Riesz operator in the plane
    Math. Ann. (IF 1.136) Pub Date : 2020-07-24
    Xiaochun Li, Shukun Wu

    We prove new \(L^p\)-estimates with \(1

    更新日期:2020-07-24
  • Gluing Delaunay ends to minimal n -noids using the DPW method
    Math. Ann. (IF 1.136) Pub Date : 2020-05-21
    Martin Traizet

    we construct constant mean curvature surfaces in euclidean space by gluing n half Delaunay surfaces to a non-degenerate minimal n-noid, using the DPW method.

    更新日期:2020-07-23
  • A reformulation of the Siegel series and intersection numbers
    Math. Ann. (IF 1.136) Pub Date : 2020-05-15
    Sungmun Cho, Takuya Yamauchi

    In this paper, we will explain a conceptual reformulation and inductive formula of the Siegel series. Using this, we will explain that both sides of the local intersection multiplicities of Gross and Keating (Invent Math 112(225–245):2051, 1993) and the Siegel series have the same inherent structures, beyond matching values. As an application, we will prove a new identity between the intersection number

    更新日期:2020-07-23
  • Quasiconvexity in 3-manifold groups
    Math. Ann. (IF 1.136) Pub Date : 2020-07-14
    Hoang Thanh Nguyen, Hung Cong Tran, Wenyuan Yang

    In this paper, we study strongly quasiconvex subgroups in a finitely generated 3-manifold group \(\pi _1(M)\). We prove that if M is a compact, orientable 3-manifold that does not have a summand supporting the Sol geometry in its sphere-disc decomposition then a finitely generated subgroup \(H \le \pi _1(M)\) has finite height if and only if H is strongly quasiconvex. On the other hand, if M has a

    更新日期:2020-07-14
  • Elliptic classes of Schubert varieties
    Math. Ann. (IF 1.136) Pub Date : 2020-07-13
    Shrawan Kumar, Richárd Rimányi, Andrzej Weber

    We introduce new notions in elliptic Schubert calculus: the (twisted) Borisov–Libgober classes of Schubert varieties in general homogeneous spaces G/P. While these classes do not depend on any choice, they depend on a set of new variables. For the definition of our classes we calculate multiplicities of some divisors in Schubert varieties, which were only known for full flag varieties before. Our approach

    更新日期:2020-07-13
  • Analytical shape recovery of a conductivity inclusion based on Faber polynomials
    Math. Ann. (IF 1.136) Pub Date : 2020-07-10
    Doosung Choi, Junbeom Kim, Mikyoung Lim

    A conductivity inclusion, inserted in a homogeneous background, induces a perturbation in the background potential. This perturbation admits a multipole expansion whose coefficients are the so-called generalized polarization tensors (GPTs). GPTs can be obtained from multistatic measurements. As a modification of GPTs, the Faber polynomial polarization tensors (FPTs) were recently introduced in two

    更新日期:2020-07-10
  • Reflection maps
    Math. Ann. (IF 1.136) Pub Date : 2020-07-09
    Guillermo Peñafort Sanchis

    Given a reflection group G acting on a complex vector space V, a reflection map is the composition of an embedding \(X \hookrightarrow V\) with the quotient map \(V\rightarrow \mathbb {C}^p\) of G. We show how these maps, which can highly singular, may be studied in terms of the group action. We give obstructions to \(\mathcal {A}\)-stability and \(\mathcal {A}\)-finiteness of reflection maps and produce

    更新日期:2020-07-09
  • Quantitative non-vanishing of Dirichlet L -values modulo p
    Math. Ann. (IF 1.136) Pub Date : 2020-07-09
    Ashay Burungale, Hae-Sang Sun

    Let p be an odd prime and k a non-negative integer. Let N be a positive integer such that \(p \not \mid N\) and \(\lambda \) a Dirichlet character modulo N. We obtain quantitative lower bounds for the number of Dirichlet character \(\chi \) modulo F with the critical Dirichlet L-value \(L(-k,\lambda \chi )\) being p-indivisible. Here \(F \rightarrow \infty \) with \((N,F)=1\) and \(p\not \mid F\phi

    更新日期:2020-07-09
  • The unirationality of the moduli space of K 3 surfaces of genus 22
    Math. Ann. (IF 1.136) Pub Date : 2020-07-09
    Gavril Farkas, Alessandro Verra

    Using the connection discovered by Hassett between the Noether-Lefschetz moduli space \(\mathcal {C}_{42}\) of special cubic fourfolds of discriminant 42 and the moduli space \(\mathcal {F}_{22}\) of polarized K3 surfaces of genus 22, we show that the universal K3 surface over \(\mathcal {F}_{22}\) is unirational.

    更新日期:2020-07-09
  • The uniqueness of inverse problems for a fractional equation with a single measurement
    Math. Ann. (IF 1.136) Pub Date : 2020-07-09
    Yavar Kian, Zhiyuan Li, Yikan Liu, Masahiro Yamamoto

    This article is concerned with an inverse problem on simultaneously determining some unknown coefficients and/or an order of derivative in a multidimensional time-fractional evolution equation either in a Euclidean domain or on a Riemannian manifold. Based on a special choice of the Dirichlet boundary input, we prove the unique recovery of at most two out of four \(\varvec{x}\)-dependent coefficients

    更新日期:2020-07-09
  • Good recursive towers over prime fields exist
    Math. Ann. (IF 1.136) Pub Date : 2020-07-09
    Alp Bassa, Christophe Ritzenthaler

    We give a construction and equations for good recursive towers over any finite field \(\mathbf {F}_q\) with \(q \ne 2\) and 3.

    更新日期:2020-07-09
  • BV functions in Hilbert spaces
    Math. Ann. (IF 1.136) Pub Date : 2020-07-09
    Giuseppe Da Prato, Alessandra Lunardi

    We study the basic theory of BV functions in a Hilbert space X endowed with a (not necessarily Gaussian) probability measure \(\nu \). We present necessary and sufficient conditions in order that a function \(u\in L^p(X, \nu )\) is of bounded variation. We also discuss the De Giorgi approach to BV functions through the behavior as \(t\rightarrow 0\) of \(\int _X \Vert \nabla T(t)u\Vert \,d\nu \), for

    更新日期:2020-07-09
  • Cartan subalgebras and the UCT problem, II
    Math. Ann. (IF 1.136) Pub Date : 2020-07-06
    Selçuk Barlak, Xin Li

    We study the connection between the UCT problem and Cartan subalgebras in C*-algebras. The UCT problem asks whether every separable nuclear C*-algebra satisfies the UCT, i.e., a noncommutative analogue of the classical universal coefficient theorem from algebraic topology. This UCT problem is one of the remaining major open questions in the structure and classification theory of simple nuclear C*-algebras

    更新日期:2020-07-06
  • About local continuity with respect to $$L_{2}$$ L 2 initial data for energy solutions of the Navier–Stokes equations
    Math. Ann. (IF 1.136) Pub Date : 2020-07-03
    Tobias Barker

    In this paper we consider classes of initial data that ensure local-in-time Hadamard well-posedness of the associated weak Leray–Hopf solutions of the three-dimensional Navier–Stokes equations. In particular, for any solenodial \(L_{2}\) initial data \(u_{0}\) belonging to certain subsets of \(VMO^{-1}(\mathbb {R}^3)\), we show that weak Leray–Hopf solutions depend continuously with respect to small

    更新日期:2020-07-03
  • The enough g -pairs property and denominator vectors of cluster algebras
    Math. Ann. (IF 1.136) Pub Date : 2020-07-02
    Peigen Cao, Fang Li

    In this paper, we introduce the enough g-pairs property for principal coefficients cluster algebras, which can be understood as a strong version of the sign-coherence of the G-matrices. Then we prove that any skew-symmetrizable principal coefficients cluster algebra has the enough g-pairs property. As applications, we prove some long standing conjectures in cluster algebras, including a conjecture

    更新日期:2020-07-02
  • Asymptotic behavior of solutions to elliptic and parabolic equations with unbounded coefficients of the second order in unbounded domains
    Math. Ann. (IF 1.136) Pub Date : 2020-07-02
    Hideo Kozono, Yutaka Terasawa, Yuta Wakasugi

    We study an asymptotic behavior of solutions to elliptic equations of the second order in a two dimensional exterior domain. Under the assumption that the solution belongs to \(L^q\) with \(q \in [2,\infty )\), we prove a pointwise asymptotic estimate of the solution at the spatial infinity in terms of the behavior of the coefficients. As a corollary, we obtain the Liouville-type theorem in the case

    更新日期:2020-07-02
  • Logarithmic Kodaira dimension and zeros of holomorphic log-one-forms
    Math. Ann. (IF 1.136) Pub Date : 2020-06-30
    Chuanhao Wei

    In this paper, we prove that the zero-locus of any global holomorphic log-one-form on a projective log-smooth pair (X; D) of log-general type must be non-empty.

    更新日期:2020-06-30
  • A diagrammatic approach to the AJ Conjecture
    Math. Ann. (IF 1.136) Pub Date : 2020-06-25
    Renaud Detcherry, Stavros Garoufalidis

    The AJ Conjecture relates a quantum invariant, a minimal order recursion for the colored Jones polynomial of a knot (known as the \(\hat{A}\) polynomial), with a classical invariant, namely the defining polynomial A of the \({\mathrm {PSL}_2(\mathbb {C})}\) character variety of a knot. More precisely, the AJ Conjecture asserts that the set of irreducible factors of the \(\hat{A}\)-polynomial (after

    更新日期:2020-06-25
  • Strong unique continuation for the Lamé system with less regular coefficients
    Math. Ann. (IF 1.136) Pub Date : 2020-06-19
    Blair Davey, Ching-Lung Lin, Jenn-Nan Wang

    We study the strong unique continuation property (SUCP) for the Lamé system in the plane. The main contribution of our work is to prove that the SUCP holds when Lamé coefficients \((\mu ,\lambda )\in W^{2,s}(\Omega )\times L^\infty (\Omega )\) for some \(s>4/3\). In other words, we establish the SUCP for the Lamé system in the plane when \(\lambda \) is bounded and \(\mu \) belongs to certain Hölder

    更新日期:2020-06-19
  • Rank n swapping algebra for $${\text {PGL}}_n$$PGLn Fock–Goncharov $$\mathcal {X}$$X moduli space
    Math. Ann. (IF 1.136) Pub Date : 2020-06-18
    Zhe Sun

    The ranknswapping multifraction algebra is a field of cross ratios up to \((n+1)\times (n+1)\)-determinant relations equipped with a Poisson bracket, called the swapping bracket, defined on the set of ordered pairs of points of a circle using linking numbers. Let \(D_k\) be a disk with k points on its boundary. The moduli space \(\mathcal {X}_{{\text {PGL}}_n,D_k}\) is the building block of the Fock–Goncharov

    更新日期:2020-06-18
  • The Gursky–Streets equations
    Math. Ann. (IF 1.136) Pub Date : 2020-06-17
    Weiyong He

    Gursky–Streets introduced a formal Riemannian metric on the space of conformal metrics in a fixed conformal class of a compact Riemannian four-manifold in the context of the \(\sigma _2\)-Yamabe problem. The geodesic equation of Gursky–Streets’ metric is a fully nonlinear degenerate elliptic equation. Using this geometric structure and the geodesic equation, Gursky–Streets proved an important result

    更新日期:2020-06-17
  • Unlikely intersections with isogeny orbits in a product of elliptic schemes
    Math. Ann. (IF 1.136) Pub Date : 2020-06-17
    Gabriel A. Dill

    Fix an elliptic curve \(E_0\) without CM and a non-isotrivial elliptic scheme over a smooth irreducible curve, both defined over the algebraic numbers. Consider the union of all images of a fixed finite-rank subgroup (of arbitrary rank) of \(E_0^g\), also defined over the algebraic numbers, under all isogenies between \(E_0^g\) and some fiber of the g-th fibered power \(\mathcal {A}\) of the elliptic

    更新日期:2020-06-17
  • Energy quantization for a singular super-Liouville boundary value problem
    Math. Ann. (IF 1.136) Pub Date : 2020-06-16
    Jürgen Jost, Chunqin Zhou, Miaomiao Zhu

    In this paper, we develop the blow-up analysis and establish the energy quantization for solutions to super-Liouville type equations on Riemann surfaces with conical singularities at the boundary. In other problems in geometric analysis, the blow-up analysis usually strongly utilizes conformal invariance, which yields a Noether current from which strong estimates can be derived. Here, however, the

    更新日期:2020-06-16
  • Vortex stretching and enhanced dissipation for the incompressible 3D Navier–Stokes equations
    Math. Ann. (IF 1.136) Pub Date : 2020-06-15
    In-Jee Jeong, Tsuyoshi Yoneda

    We consider the 3D incompressible Navier–Stokes equations under the following \(2+\frac{1}{2}\)-dimensional situation: small-scale horizontal vortex blob being stretched by large-scale, anti-parallel pairs of vertical vortex tubes. We prove enhanced dissipation induced by such vortex-stretching.

    更新日期:2020-06-15
  • Differences between fundamental solutions of general higher order elliptic operators and of products of second order operators
    Math. Ann. (IF 1.136) Pub Date : 2020-06-11
    Hans-Christoph Grunau, Giulio Romani, Guido Sweers

    We study fundamental solutions of elliptic operators of order \(2m\ge 4\) with constant coefficients in large dimensions \(n\ge 2m\), where their singularities become unbounded. For compositions of second order operators these can be chosen as convolution products of positive singular functions, which are positive themselves. As soon as \(n\ge 3\), the polyharmonic operator \((-\Delta )^m\) may no

    更新日期:2020-06-11
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