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  • On the dimension of voisin sets in the moduli space of abelian varieties
    Math. Ann. (IF 1.136) Pub Date : 2021-01-12
    E. Colombo, J. C. Naranjo, G. P. Pirola

    We study the subsets \(V_k(A)\) of a complex abelian variety A consisting in the collection of points \(x\in A\) such that the zero-cycle \(\{x\}-\{0_A\}\) is k-nilpotent with respect to the Pontryagin product in the Chow group. These sets were introduced recently by Voisin and she showed that \(\dim V_k(A) \le k-1\) and \(\dim V_k(A)\) is countable for a very general abelian variety of dimension at

  • p -adic étale cohomology of period domains
    Math. Ann. (IF 1.136) Pub Date : 2021-01-12
    Pierre Colmez, Gabriel Dospinescu, Julien Hauseux, Wiesława Nizioł

    We compute the p-torsion and p-adic étale cohomologies with compact support of period domains over local fields in the case of basic isocrystals for quasi-split reductive groups. As in the cases of \(\ell \)-torsion or \(\ell \)-adic coefficients, \(\ell \ne p\), considered by Orlik, the results involve generalized Steinberg representations. For the p-torsion case, we follow the method used by Orlik

  • The Dirichlet principle for inner variations
    Math. Ann. (IF 1.136) Pub Date : 2021-01-12
    Tadeusz Iwaniec, Jani Onninen

    We are concerned with the Dirichlet energy of mappings defined on domains in the complex plane. The Dirichlet Principle, the name coined by Riemann, tells us that the outer variation of a harmonic mapping increases its energy. Surprisingly, when one jumps into details about inner variations, which are just a change of independent variables, new equations and related questions start to matter. The inner

  • An asymptotic vanishing theorem for the cohomology of thickenings
    Math. Ann. (IF 1.136) Pub Date : 2021-01-12
    Bhargav Bhatt, Manuel Blickle, Gennady Lyubeznik, Anurag K. Singh, Wenliang Zhang

    Let X be a closed equidimensional local complete intersection subscheme of a smooth projective scheme Y over a field, and let \(X_t\) denote the t-th thickening of X in Y. Fix an ample line bundle \(\mathcal {O}_Y(1)\) on Y. We prove the following asymptotic formulation of the Kodaira vanishing theorem: there exists an integer c, such that for all integers \(t \geqslant 1\), the cohomology group \(H^k(X_t

  • Tomography bounds for the Fourier extension operator and applications
    Math. Ann. (IF 1.136) Pub Date : 2021-01-12
    Jonathan Bennett, Shohei Nakamura

    We explore the extent to which the Fourier transform of an \(L^p\) density supported on the sphere in \(\mathbb {R}^n\) can have large mass on affine subspaces, placing particular emphasis on lines and hyperplanes. This involves establishing bounds on quantities of the form \(X(|\widehat{gd\sigma }|^2)\) and \(\mathcal {R}(|\widehat{gd\sigma }|^2)\), where X and \(\mathcal {R}\) denote the X-ray and

  • Affinoids in the Lubin–Tate perfectoid space and simple supercuspidal representations II: wild case
    Math. Ann. (IF 1.136) Pub Date : 2021-01-09
    Naoki Imai, Takahiro Tsushima

    We construct a family of affinoids in the Lubin–Tate perfectoid space and their formal models such that the middle cohomology of their reductions realizes the local Langlands correspondence and the local Jacquet–Langlands correspondence for the simple supercuspidal representations. The reductions of the formal models are isomorphic to the perfections of some Artin–Schreier varieties, whose cohomology

  • A topological invariant for continuous fields of Cuntz algebras
    Math. Ann. (IF 1.136) Pub Date : 2021-01-09
    Taro Sogabe

    We wish to investigate continuous fields of the Cuntz algebras. The Cuntz algebras \({\mathcal {O}}_{n+1}, n\ge 1\) play an important role in the theory of operator algebras, and they are characterized by their K-groups \(K_0({\mathcal {O}}_{n+1})={\mathbb {Z}}_n\), the cyclic groups of order \(n\ge 1\). Since the mod n K-group for a compact Hausdorff space can be realized by the K-group of the trivial

  • An arithmetic enrichment of Bézout’s Theorem
    Math. Ann. (IF 1.136) Pub Date : 2021-01-09
    Stephen McKean

    The classical version of Bézout’s Theorem gives an integer-valued count of the intersection points of hypersurfaces in projective space over an algebraically closed field. Using work of Kass and Wickelgren, we prove a version of Bézout’s Theorem over any perfect field by giving a bilinear form-valued count of the intersection points of hypersurfaces in projective space. Over non-algebraically closed

  • Mapping class groups, multiple Kodaira fibrations, and CAT(0) spaces
    Math. Ann. (IF 1.136) Pub Date : 2021-01-09
    Claudio Llosa Isenrich, Pierre Py

    We study several geometric and group theoretical problems related to Kodaira fibrations, to more general families of Riemann surfaces, and to surface-by-surface groups. First we provide constraints on Kodaira fibrations that fiber in more than two distinct ways, addressing a question by Catanese and Salter about their existence. Then we show that if the fundamental group of a surface bundle over a

  • Signs of Fourier coefficients of half-integral weight modular forms
    Math. Ann. (IF 1.136) Pub Date : 2021-01-09
    Stephen Lester, Maksym Radziwiłł

    Let g be a Hecke cusp form of half-integral weight, level 4 and belonging to Kohnen’s plus subspace. Let c(n) denote the nth Fourier coefficient of g, normalized so that c(n) is real for all \(n \ge 1\). A theorem of Waldspurger determines the magnitude of c(n) at fundamental discriminants n by establishing that the square of c(n) is proportional to the central value of a certain L-function. The signs

  • Bergman–Weil expansion for holomorphic functions
    Math. Ann. (IF 1.136) Pub Date : 2021-01-09
    Alekos Vidras, Alain Yger

    Using a modified Cauchy–Weil representation formula in a Weil polyhedron \({\varvec{D}}_f\subset U\subset \mathbb {C}^n\), we prove a generalized version of Lagrange interpolation formula (at any order) with respect to a discrete set defined by \(V_{{\varvec{D}}_f}(f):=\{f_1=\cdots = f_m =0\}\, \cap {\varvec{D}}_f\), when \(m>n\) and \(\{f_1,\ldots ,f_m\}\) is minimal as a defining system. Thus the

  • Gromov hyperbolicity of pseudoconvex finite type domains in $${\mathbb {C}}^2$$ C 2
    Math. Ann. (IF 1.136) Pub Date : 2021-01-09
    Matteo Fiacchi

    We prove that every bounded smooth domain of finite D’Angelo type in \({\mathbb {C}}^2\) endowed with the Kobayashi distance is Gromov hyperbolic and its Gromov boundary is canonically homeomorphic to the Euclidean boundary. We also show that any domain in \({\mathbb {C}}^2\) endowed with the Kobayashi distance is Gromov hyperbolic provided there exists a sequence of automorphisms that converges to

  • Coriolis effect on temporal decay rates of global solutions to the fractional Navier–Stokes equations
    Math. Ann. (IF 1.136) Pub Date : 2021-01-09
    Jaewook Ahn, Junha Kim, Jihoon Lee

    The incompressible fractional Navier–Stokes equations in the rotational framework is considered. We establish the global existence result and temporal decay estimate for a unique smooth solution when the speed of rotation is sufficiently rapid. It is found that the strong rotational effect enhances the temporal decay rate of a certain norm of the velocity.

  • Liouville results for fully nonlinear equations modeled on Hörmander vector fields: I. The Heisenberg group
    Math. Ann. (IF 1.136) Pub Date : 2020-12-23
    Martino Bardi, Alessandro Goffi

    This paper studies Liouville properties for viscosity sub- and supersolutions of fully nonlinear degenerate elliptic PDEs, under the main assumption that the operator has a family of generalized subunit vector fields that satisfy the Hörmander condition. A general set of sufficient conditions is given such that all subsolutions bounded above are constant; it includes the existence of a supersolution

  • On generating functions in additive number theory, II: lower-order terms and applications to PDEs
    Math. Ann. (IF 1.136) Pub Date : 2020-12-23
    J. Brandes, S. T. Parsell, C. Poulias, G. Shakan, R. C. Vaughan

    We obtain asymptotics for sums of the form $$\begin{aligned} \sum _{n=1}^P e\left( {\alpha }_k\,n^k\,+\,{\alpha }_1 n\right) , \end{aligned}$$ involving lower order main terms. As an application, we show that for almost all \({\alpha }_2 \in [0,1)\) one has $$\begin{aligned} \sup _{{\alpha }_{1} \in [0,1)} \Big | \sum _{1 \le n \le P} e\left( {\alpha }_{1}\left( n^{3}+n\right) + {\alpha }_{2} n^{3}\right)

  • Averages and higher moments for the $$\ell $$ ℓ -torsion in class groups
    Math. Ann. (IF 1.136) Pub Date : 2020-12-23
    Christopher Frei, Martin Widmer

    We prove upper bounds for the average size of the \(\ell \)-torsion \({{\,\mathrm{Cl}\,}}_K[\ell ]\) of the class group of K, as K runs through certain natural families of number fields and \(\ell \) is a positive integer. We refine a key argument, used in almost all results of this type, which links upper bounds for \({{\,\mathrm{Cl}\,}}_K[\ell ]\) to the existence of many primes splitting completely

  • Coxeter groups and meridional rank of links
    Math. Ann. (IF 1.136) Pub Date : 2020-12-23
    Sebastian Baader, Ryan Blair, Alexandra Kjuchukova

    We prove the meridional rank conjecture for twisted links and arborescent links associated to bipartite trees with even weights. These links are substantial generalizations of pretzels and two-bridge links, respectively. Lower bounds on meridional rank are obtained via Coxeter quotients of the groups of link complements. Matching upper bounds on bridge number are found using the Wirtinger numbers of

  • 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

  • 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

  • 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.

  • 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.

  • 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

  • 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)

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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.

  • 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

  • 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.

  • 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.

  • 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

  • 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

  • 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 \(L(E_D, 1)\)

  • 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.

  • 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

  • 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

  • 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

  • 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.

  • 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

  • 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.

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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)

  • 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

  • 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 \(\mathbb {R}^3_+\).

  • 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

  • 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

  • Unknottedness of real Lagrangian tori in \(S^2\times S^2\)
    Math. Ann. (IF 1.136) Pub Date : 2020-07-27
    Joontae Kim

    We prove the Hamiltonian unknottedness of real Lagrangian tori in the monotone \(S^2\times S^2\), namely any real Lagrangian torus in \(S^2\times S^2\) is Hamiltonian isotopic to the Clifford torus. The proof is based on a neck-stretching argument, Gromov’s foliation theorem, and the Cieliebak–Schwingenheuer criterion.

  • 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

  • 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.

  • 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

  • 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

  • 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

  • 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

  • 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

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