• 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 • 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 • 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 • 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 • 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
• 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
• 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
• 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
• 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 • 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• Math. Ann. (IF 1.136) Pub Date : 2020-06-08
Diarmuid Crowley, Johannes Nordström

We exhibit the first examples of closed 7-dimensional Riemannian manifolds with holonomy $$G_2$$ that are homeomorphic but not diffeomorphic. These are also the first examples of closed Ricci-flat manifolds that are homeomorphic but not diffeomorphic. The examples are generated by applying the twisted connected sum construction to Fano 3-folds of Picard rank 1 and 2. The smooth structures are distinguished

更新日期：2020-06-08
• Math. Ann. (IF 1.136) Pub Date : 2020-06-06
Timothée Marquis, Marcin Sabok

We prove that for every finitely generated hyperbolic group G, the action of G on its Gromov boundary induces a hyperfinite equivalence relation.

更新日期：2020-06-06
• Math. Ann. (IF 1.136) Pub Date : 2020-06-04
Linquan Ma, Pham Hung Quy, Ilya Smirnov

We answer affirmatively a question of Srinivas–Trivedi (J Algebra 186(1):1–19, 1996): in a Noetherian local ring $$(R,{{\,\mathrm{\mathfrak {m}}\,}})$$, if $$f_1,\dots ,f_r$$ is a filter-regular sequence and J is an ideal such that $$(f_1, \ldots , f_r)+J$$ is $${{\,\mathrm{\mathfrak {m}}\,}}$$-primary, then there exists $$N>0$$ such that for any $$\varepsilon _1,\dots ,\varepsilon _r \in {{\,\mathrm{\mathfrak 更新日期：2020-06-04 • Math. Ann. (IF 1.136) Pub Date : 2020-06-04 Jann-Long Chern, Eiji Yanagida We consider the structure of radially symmetric singular solutions for elliptic equations with the Hardy term and power nonlinearity. In the critical case, it is shown that there exists a unique non-oscillatory singular solution, around which infinitely many singular solutions are oscillating. We also study the subcritical and supercritical cases and make clear the difference of structure from the 更新日期：2020-06-04 • Math. Ann. (IF 1.136) Pub Date : 2020-06-03 Peng Chen, Xuan Thinh Duong, Ji Li, Lixin Yan Let L be a non-negative self-adjoint operator acting on \(L^2(X)$$ where X is a space of homogeneous type with a dimension n. Suppose that the heat operator $$e^{-tL}$$ satisfies the generalized Gaussian $$(p_0, p'_0)$$-estimates of order m for some $$1\le p_0 < 2$$. In this paper we prove sharp endpoint $$L^p$$-Sobolev bound for the Schrödinger group $$e^{itL}$$, that is for every $$p\in (p_0, p'_0)$$

更新日期：2020-06-03
• Math. Ann. (IF 1.136) Pub Date : 2020-06-03
Van Hoang Nguyen

This paper is addressed to study the existence of maximizers for the singular Moser–Trudinger supremum under constraints in the critical case \begin{aligned} MT_{N}(a,\beta ) = \sup _{u\in W^{1,N}({\mathbb {R}}^N),\, \Vert \nabla u\Vert _N^a + \Vert u\Vert _N^N =1} \int _{{\mathbb {R}}^N}\Phi _N\left( (1-\beta /N)\alpha _N |u|^{\frac{N}{N-1}}\right) |x|^{-\beta } dx, \end{aligned} where $$a>0$$

更新日期：2020-06-03
• Math. Ann. (IF 1.136) Pub Date : 2020-06-03
Jaehyun Hong, Sui-Chung Ng

Let G/P be a rational homogeneous space (not necessarily irreducible) and $$x_0\in G/P$$ be the point at which the isotropy group is P. The G-translates of the orbit $$Qx_0$$ of a parabolic subgroup $$Q\subsetneq G$$ such that $$P\cap Q$$ is parabolic are called Q-cycles. We established an extension theorem for local biholomorphisms on G/P that map local pieces of Q-cycles into Q-cycles. We showed

更新日期：2020-06-03
• Math. Ann. (IF 1.136) Pub Date : 2020-06-02
Ki-Ahm Lee, Jinwan Park

In this paper, we study the regularity of the free boundaries of the parabolic double obstacle problem for the heat operator and fully nonlinear operator. The result in this paper are generalizations of the theory for the elliptic problem in Lee et al. (Calc Var Partial Differ Equ 58(3):104, 2019) and Lee and Park (The regularity theory for the double obstacle problem for fully nonlinear operator,

更新日期：2020-06-02
• Math. Ann. (IF 1.136) Pub Date : 2020-05-14
Emma Brakkee

Motivated by the relation between (twisted) K3 surfaces and special cubic fourfolds, we construct moduli spaces of polarized twisted K3 surfaces of any fixed degree and order. We do this by mimicking the construction of the moduli space of untwisted polarized K3 surfaces as a quotient of a bounded symmetric domain.

更新日期：2020-05-14
• Math. Ann. (IF 1.136) Pub Date : 2020-05-08
Damien Roy

We show that Hermite’s approximations to values of the exponential function at given algebraic numbers are nearly optimal when considered from an adelic perspective. We achieve this by taking into account the ratio of these values whenever they make sense in the various completions (Archimedean or p-adic) of a number field containing these algebraic numbers.

更新日期：2020-05-08
• Math. Ann. (IF 1.136) Pub Date : 2020-05-07
Raphael S. Steiner

We prove sub-convex bounds on the fourth moment of Hecke–Laplace eigenforms on $$S^3$$. As a corollary, we get a Burgess-type sub-convex bound on the sup-norm of an individual eigenform. This constitutes an improvement over what is achievable through employing the Iwaniec–Sarnak amplifier.

更新日期：2020-05-07
• Math. Ann. (IF 1.136) Pub Date : 2020-05-02
Man-Chun Lee

In this work, we show that along a particular choice of Hermitian curvature flow, the non-positivity of the first Ricci curvature will be preserved if the initial metric has Griffiths non-positive Chern curvature. If in addition, the first Ricci curvature is negative at a point, then the canonical line bundle is ample.

更新日期：2020-05-02
• Math. Ann. (IF 1.136) Pub Date : 2020-04-28
Antonio Alfieri, Sungkyung Kang, András I. Stipsicz

Using the covering involution on the double branched cover of $$S^3$$ branched along a knot, and adapting ideas of Hendricks–Manolescu and Hendricks–Hom–Lidman, we define new knot (concordance) invariants and apply them to deduce novel linear independence results in the smooth concordance group of knots.

更新日期：2020-04-28
• Math. Ann. (IF 1.136) Pub Date : 2020-04-28
Octave Curmi

We prove that the boundaries of the Milnor fibers of smoothings of non-isolated reduced complex surface singularities are graph manifolds. Moreover, we give a method, inspired by previous work of Némethi and Szilard, to compute associated plumbing graphs.

更新日期：2020-04-28
• Math. Ann. (IF 1.136) Pub Date : 2020-04-25
Benjamin Ambrosio, Arnaud Ducrot, Shigui Ruan

Traveling wave solutions in general time-dependent (including time-periodic) reaction–diffusion equations and systems of equations have attracted great attention in the last two decades. The aim of this paper is to study the propagation phenomenon in a general time-heterogeneous environment. More specifically, we investigate generalized traveling wave solutions for a two-component time-dependent non-cooperative

更新日期：2020-04-25
• Math. Ann. (IF 1.136) Pub Date : 2020-04-23
Fabien Priziac

Using the geometric quotient of a real algebraic set by the action of a finite group G, we construct invariants of G-affine real algebraic varieties with respect to equivariant homeomorphisms with algebraic graph, including additive invariants with values in $${\mathbb {Z}}$$. The construction requires to consider the wider category of $$\mathcal {AS}$$-sets.

更新日期：2020-04-23
• Math. Ann. (IF 1.136) Pub Date : 2020-04-22
Kazuki Tokimoto

Following Weinstein, Boyarchenko–Weinstein and Imai–Tsushima, we construct a family of affinoids in the Lubin–Tate perfectoid space and their formal models such that the cohomology of the reduction of each formal model realizes the local Langlands correspondence and the local Jacquet–Langlands correspondence for certain representations. In the terminology of the essentially tame local Langlands correspondence

更新日期：2020-04-23
• Math. Ann. (IF 1.136) Pub Date : 2020-04-22
Mohan Ravichandran, Jonathan Leake

We adapt the arguments of Marcus, Spielman and Srivastava in their proof of the Kadison–Singer problem to prove improved paving estimates. Working with Anderson’s paving formulation of Kadison–Singer instead of Weaver’s vector balancing version, we show that the machinery of interlacing polynomials due to Marcus, Spielman and Srivastava works in this setting as well. The relevant expected characteristic

更新日期：2020-04-23
• Math. Ann. (IF 1.136) Pub Date : 2020-04-22
Natalia Garcia-Fritz, Hector Pasten

For a positive proportion of primes p and q, we prove that $${\mathbb {Z}}$$ is Diophantine in the ring of integers of $${\mathbb {Q}}(\root 3 \of {p},\sqrt{-q})$$. This provides a new and explicit infinite family of number fields K such that Hilbert’s tenth problem for $$O_K$$ is unsolvable. Our methods use Iwasawa theory and congruences of Heegner points in order to obtain suitable rank stability

更新日期：2020-04-23
• Math. Ann. (IF 1.136) Pub Date : 2020-04-18
Elia Brué, Quoc-Hung Nguyen

It is known, after Jabin (J Differ Equ 260(5):4739–4757, 2016) and Alberti et al. (Ann PDE 5(1):9, 2019), that ODE flows and solutions of the transport equation associated to Sobolev vector fields do not propagate Sobolev regularity, even of fractional order. In this paper, we improve the result at Clop and Jylha (J Differ Equ 266(8):4544–4567, 2019) and show that some kind of propagation of Sobolev

更新日期：2020-04-23
• Math. Ann. (IF 1.136) Pub Date : 2020-04-16
Kathryn Mann, Sam Nariman

Motivated by a question of Ghys, we study obstructions to extending group actions on the boundary $$\partial M$$ of a 3-manifold to a $$C^0$$-action on M. Among other results, we show that for a 3-manifold M, the $$S^1 \times S^1$$ action on the boundary does not extend to a $$C^0$$-action of $$S^1 \times S^1$$ via homeomorphisms that are isotopic to the identity as a discrete group on M, except in

更新日期：2020-04-23
• Math. Ann. (IF 1.136) Pub Date : 2020-04-13
Chris Connell, Shi Wang

We show that any closed manifold with a metric of nonpositive curvature that admits either a single point rank condition or a single point curvature condition has positive simplicial volume. We use this to provide a differential geometric proof of a conjecture of Gromov in dimension three.

更新日期：2020-04-23
• Math. Ann. (IF 1.136) Pub Date : 2020-04-02
Cristian Minoccheri

A variety is rationally connected if two general points can be joined by a rational curve. A higher version of this notion is rational simple connectedness, which requires suitable spaces of rational curves through two points to be rationally connected themselves. We prove that smooth, complex, weighted complete intersections of low enough degree are rationally simply connected. This result has strong

更新日期：2020-04-23
• Math. Ann. (IF 1.136) Pub Date : 2020-03-16
Jacopo Bellazzini, Vladimir Georgiev, Nicola Visciglia

The assumptions of Theorem are not correct in case

更新日期：2020-04-23
• Math. Ann. (IF 1.136) Pub Date : 2019-09-13
Erik Carlsson, Eugene Gorsky, Anton Mellit

The earlier work of the first and the third name authors introduced the algebra $${\mathbb {A}}_{q,t}$$ and its polynomial representation. In this paper we construct an action of this algebra on the equivariant K-theory of certain smooth strata in the flag Hilbert scheme of points on the plane. In this presentation, the fixed points of the torus action correspond to generalized Macdonald polynomials

更新日期：2020-04-23
• Math. Ann. (IF 1.136) Pub Date : 2020-02-17
Takashi Taniguchi, Frank Thorne

In our companion paper [28], we developed an efficient algebraic method for computing the Fourier transforms of certain functions defined on prehomogeneous vector spaces over finite fields, and we carried out these computations in a variety of cases. Here we develop a method, based on Fourier analysis and algebraic geometry, which exploits these Fourier transform formulas to yield level of distribution

更新日期：2020-04-23
• Math. Ann. (IF 1.136) Pub Date : 2018-10-08
Wen-yuan Yang

We establish that, for statistically convex-cocompact actions, contracting elements are exponentially generic in counting measure. We obtain as corollaries results on the exponential genericity for the set of hyperbolic elements in relatively hyperbolic groups, the set of rank-1 elements in CAT(0) groups, and the set of pseudo-Anosov elements in mapping class groups. For a proper action with purely

更新日期：2020-04-23
• Math. Ann. (IF 1.136) Pub Date : 2019-09-18
Long Jin, Ruixiang Zhang

We prove an explicit formula for the dependence of the exponent $$\beta$$ in the fractal uncertainty principle of Bourgain–Dyatlov (Ann Math 187:1–43, 2018) on the dimension $$\delta$$ and on the regularity constant $$C_R$$ for the regular set. In particular, this implies an explicit essential spectral gap for convex co-compact hyperbolic surfaces when the Hausdorff dimension of the limit set is

更新日期：2020-04-23
• Math. Ann. (IF 1.136) Pub Date : 2019-11-27
Haining Wang

In this article we study the special fiber of the Rapoport–Zink space attached to a quaternionic unitary group. The special fiber is described using the so called Bruhat–Tits stratification and is intimately related to the Bruhat–Tits building of a split symplectic group. As an application we describe the supersingular locus of the related Shimura variety.

更新日期：2020-04-23
• Math. Ann. (IF 1.136) Pub Date : 2019-12-02
Quy Thuong Lê, Hong Duc Nguyen

We develop Denef–Loeser’s motivic integration to an equivariant version and use it to prove the full integral identity conjecture for regular functions. In comparison with Hartmann’s work, the equivariant Grothendieck ring defined in this article is more elementary and it yields the application to the conjecture.

更新日期：2020-04-23
• Math. Ann. (IF 1.136) Pub Date : 2019-10-10
Eckhard Meinrenken, María Amelia Salazar

The classical Van Est theory relates the smooth cohomology of Lie groups with the cohomology of the associated Lie algebra, or its relative versions. Some aspects of this theory generalize to Lie groupoids and their Lie algebroids. In this paper, continuing an idea from Li-Bland and Meinrenken (Enseign Math 61(1–2):93–137, 2015), we revisit the van Est theory using the Perturbation Lemma from homological

更新日期：2020-04-23
• Math. Ann. (IF 1.136) Pub Date : 2019-11-07
Ofir Gorodetsky, Will Sawin

For a fixed polynomial $$\varDelta$$, we study the number of polynomials f of degree n over $${\mathbb {F}}_q$$ such that f and $$f+\varDelta$$ are both irreducible, an $${\mathbb {F}}_q[T]$$-analogue of the twin primes problem. In the large-q limit, we obtain a lower-order term for this count if we consider non-monic polynomials, which depends on $$\varDelta$$ in a manner which is consistent with

更新日期：2020-04-23
• Math. Ann. (IF 1.136) Pub Date : 2019-09-25
David Damanik, Jake Fillman, Selim Sukhtaiev

We establish spectral and dynamical localization for several Anderson models on metric and discrete radial trees. The localization results are obtained on compact intervals contained in the complement of discrete sets of exceptional energies. All results are proved under the minimal hypothesis on the type of disorder: the random variables generating the trees assume at least two distinct values. This

更新日期：2020-04-23
• Math. Ann. (IF 1.136) Pub Date : 2019-02-15
Federico Cacciafesta, Anne-Sophie de Suzzoni, Diego Noja

The system describing a single Dirac electron field coupled with classically moving point nuclei is presented and studied. The model is a semi-relativistic extension of corresponding time-dependent one-body Hartree-Fock equation coupled with classical nuclear dynamics, already known and studied both in quantum chemistry and in rigorous mathematical literature. We prove local existence of solutions

更新日期：2020-04-23
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