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p-adic families of automorphic forms in the µ-ordinary setting Am. J. Math. (IF 1.711) Pub Date : 2021-01-08 E. Eischen; E. Mantovan
abstract: We develop a theory of $p$-adic automorphic forms on unitary groups that allows $p$-adic interpolation in families and holds for all primes $p$ that do not ramify in the reflex field $E$ of the associated unitary Shimura variety. If the ordinary locus is nonempty (a condition only met if $p$ splits completely in $E$), we recover Hida's theory of $p$-adic automorphic forms, which is defined
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Symmetric convex sets with minimal Gaussian surface area Am. J. Math. (IF 1.711) Pub Date : 2021-01-08 Steven Heilman
abstract: Let $\Omega\subset\Bbb{R}^{n+1}$ have minimal Gaussian surface area among all sets satisfying $\Omega=-\Omega$ with fixed Gaussian volume. Let $A=A_x$ be the second fundamental form of $\partial\Omega$ at $x$, i.e., $A$ is the matrix of first order partial derivatives of the unit normal vector at $x\in\partial\Omega$. For any $x=(x_1,\ldots,x_{n+1})\in\Bbb{R}^{n+1}$, let $\gamma_n(x)=(2\
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Quasiconvexity and Dehn filling Am. J. Math. (IF 1.711) Pub Date : 2021-01-08 Daniel Groves; Jason Fox Manning
abstract: We define a new condition on relatively hyperbolic Dehn filling which allows us to control the behavior of a relatively quasiconvex subgroups which need not be full. As an application, in combination with recent work of Cooper and Futer, we provide a new proof of the virtual fibering of non-compact finite-volume hyperbolic $3$-manifolds, a result first proved by Wise. Additionally, we explain
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Selmer groups of symmetric powers of ordinary modular Galois representations Am. J. Math. (IF 1.711) Pub Date : 2021-01-08 Xiaoyu Zhang
abstract: Let $p$ be a fixed odd prime number, $\mu$ be a Hida family over the Iwasawa algebra of one variable, $\rho_{\mu}$ its Galois representation, $\Bbb{Q}_\infty/\Bbb{Q}$ the $p$-cyclotomic tower and $S$ the variable of the cyclotomic Iwasawa algebra. We compare, for $n\leq 4$ and under certain assumptions, the characteristic power series $L(S)$ of the dual of Selmer groups $\textrm{Sel}(\Bbb{Q}_{\infty}
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Weighted restriction estimates and application to Falconer distance set problem Am. J. Math. (IF 1.711) Pub Date : 2021-01-08 Xiumin Du; Larry Guth; Yumeng Ou; Hong Wang; Bobby Wilson; Ruixiang Zhang
abstract: We prove some weighted Fourier restriction estimates using polynomial partitioning and refined Strichartz estimates. As application we obtain improved spherical average decay rates of the Fourier transform of fractal measures, and therefore improve the results for the Falconer distance set conjecture in three and higher dimensions.
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A generalized Schmidt subspace theorem for closed subschemes Am. J. Math. (IF 1.711) Pub Date : 2021-01-08 Gordon Heier; Aaron Levin
abstract: We prove a generalized version of Schmidt's subspace theorem for closed subschemes in general position in terms of suitably defined Seshadri constants with respect to a fixed ample divisor. Our proof builds on previous work of Evertse and Ferretti, Corvaja and Zannier, and others, and uses standard techniques from algebraic geometry such as notions of positivity, blowing-ups and direct image
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Geometry of Lagrangian self-shrinking tori and applications to the piecewise Lagrangian mean curvature flow Am. J. Math. (IF 1.711) Pub Date : 2021-01-08 Jingyi Chen; John Man Shun Ma
abstract: We study geometric properties of the Lagrangian self-shrinking tori in $\Bbb{R}^4$. When the area is bounded above uniformly, we prove that the entropy for the Lagrangian self-shrinking tori can only take finitely many values; this is done by deriving a {\L}ojasiewicz-Simon type gradient inequality for the branched conformal self-shrinking tori and then combining with a compactness theorem
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Bounded strictly pseudoconvex domains in C2 with obstruction flat boundary Am. J. Math. (IF 1.711) Pub Date : 2021-01-08 Sean N. Curry; Peter Ebenfelt
abstract: On a bounded strictly pseudoconvex domain in $\Bbb{C}^n$, $n>1$, the smoothness of the Cheng-Yau solution to Fefferman's complex Monge-Ampere equation up to the boundary is obstructed by a local curvature invariant of the boundary. For bounded strictly pseudoconvex domains in $\Bbb{C}^2$ which are diffeomorphic to the ball, we motivate and consider the problem of determining whether the global
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Quasi-Harnack inequality Am. J. Math. (IF 1.711) Pub Date : 2021-01-08 D. De Silva; O. Savin
abstract: In this paper we obtain some extensions of the classical Krylov-Safonov Harnack inequality. The novelty is that we consider functions that do not necessarily satisfy an infinitesimal equation but rather exhibit a two-scale behavior. We require that at scale larger than some $r_0>0$ (small) the functions satisfy the comparison principle with a standard family of quadratic polynomials, while
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Deformations of Saito-Kurokawa type and the Paramodular Conjecture Am. J. Math. (IF 1.711) Pub Date : 2020-11-17 Tobias Berger; Krzyszto Klosin
Abstract: We study short crystalline, minimal, essentially self-dual deformations of a mod $p$ non-semisimple Galois representation $\overline{\sigma}$ with $\overline{\sigma}^{{\rm ss}}=\chi^{k-2}\oplus\rho\oplus\chi^{k-1}$, where $\chi$ is the mod $p$ cyclotomic character and $\rho$ is an absolutely irreducible reduction of the Galois representation $\rho_f$ attached to a cusp form $f$ of weight
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Endpoint Lebesgue estimates for weighted averages on polynomial curves Am. J. Math. (IF 1.711) Pub Date : 2020-11-11 Michael Christ; Spyridon Dendrinos; Betsy Stovall; Brian Street
Abstract: We establish optimal Lebesgue estimates for a class of generalized Radon transforms defined by averaging functions along polynomial-like curves. The presence of an essentially optimal weight allows us to prove uniform estimates, wherein the Lebesgue exponents are completely independent of the curves and the operator norms depend only on the polynomial degree. Moreover, our weighted estimates
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Loose crystalline lifts and overconvergence of étale (φ, τ)-modules Am. J. Math. (IF 1.711) Pub Date : 2020-11-11 Hui Gao; Tong Liu
Abstract: Let $p$ be a prime, $K$ a finite extension of $\\Bbb\{Q\}_p$, and let $G_K$ be the absolute Galois group of $K$. The category of \\'etale $(\\varphi,\\tau)$-modules is equivalent to the category of $p$-adic Galois representations of $G_K$. In this paper, we show that all \\'etale $(\\varphi,\\tau)$-modules are overconvergent; this answers a question of Caruso. Our result is an analogue of
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Compact singular minimal surfaces with boundary Am. J. Math. (IF 1.711) Pub Date : 2020-11-11 Rafael López
Abstract: We study the shape of a compact singular minimal surface in terms of the geometry of its boundary, asking what type of \{\\it a priori\} information can be obtained on the surface from the knowledge of its boundary. We derive estimates of the area and the height in terms of the boundary. In case that the boundary is a circle, we study under what conditions the surface is rotational. Finally
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On upper bounds of arithmetic degrees Am. J. Math. (IF 1.711) Pub Date : 2020-11-11 Yohsuke Matsuzawa
Abstract: Let $X$ be a smooth projective variety defined over $\\overline\{\\Bbb\{Q\}\}$, and $f\\colon X\\dashrightarrow X$ be a dominant rational map. Let $\\delta_f$ be the first dynamical degree of $f$ and $h_X\\colon X(\\overline\{\\Bbb\{Q\}\})\\rightarrow [1,\\infty)$ be a Weil height function on $X$ associated with an ample divisor on $X$. We prove several inequalities which give upper bounds
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Diameter and curvature control under mean curvature flow Am. J. Math. (IF 1.711) Pub Date : 2020-11-11 Panagiotis Gianniotis; Robert Haslhofer
Abstract: We prove that for the mean curvature flow of two-convex hypersurfaces the intrinsic diameter stays uniformly controlled as one approaches the first singular time. We also derive sharp $L^\{n-1\}$-estimates for the regularity scale of the level set flow with two-convex initial data. The results, which seem new even in the most classical case of mean convex surfaces evolving by mean curvature
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Asymptotic structure of almost eigenfunctions of drift Laplacians on conical ends Am. J. Math. (IF 1.711) Pub Date : 2020-11-11 Jacob Bernstein
Abstract: We use a weighted variant of the frequency functions introduced by Almgren to prove sharp asymptotic estimates for almost eigenfunctions of the drift Laplacian associated to the Gaussian weight on an asymptotically conical end. As a consequence, we obtain a purely elliptic proof of a result of L. Wang on the uniqueness of self-shrinkers of the mean curvature flow asymptotic to a given cone
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Uncountably many quasi-isometry classes of groups of type FP Am. J. Math. (IF 1.711) Pub Date : 2020-11-11 Robert P. Kropholler; Ian J. Leary; Ignat Soroko
Abstract: In an earlier paper, one of the authors constructed uncountable families of groups of type $FP$ and of $n$-dimensional Poincar\\'e duality groups for each $n\\geq 4$. We show that those groups comprise uncountably many quasi-isometry classes. We deduce that for each $n\\geq 4$ there are uncountably many quasi-isometry classes of acyclic $n$-manifolds admitting free cocompact properly discontinuous
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Optimal density for values of generic polynomial maps Am. J. Math. (IF 1.711) Pub Date : 2020-11-11 Anish Ghosh; Alexander Gorodnik; Amos Nevo
Abstract: We establish that the optimal bound for the size of the smallest integral solution of the Oppenheim Diophantine approximation problem $|Q(x)-\\xi|<\\epsilon$ for a generic ternary form $Q$ is $|x|\\ll\\epsilon^\{-1\}$. We also establish an optimal rate of density for the values of polynomials maps in a number of other natural problems, including the values of linear forms restricted to suitable
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Compact embedded surfaces with constant mean curvature in $\Bbb{S}^2\times\Bbb{R}$ Am. J. Math. (IF 1.711) Pub Date : 2020-11-11 José M. Manzano; Francisco Torralbo
Abstract: We obtain compact orientable embedded surfaces with constant mean curvature $0
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American Journal of Mathematics: Founded in 1878 by Johns Hopkins University Am. J. Math. (IF 1.711) Pub Date : 2020-11-11
AMERICAN JOURNAL OF MATHEMATICS Founded in 1878 by Johns Hopkins University INDEX TO VOLUME 142 2020 PAGE BECEANU, M. and W. SCHLAG. Structure formulas for wave operators . 751 BERGER, TOBIAS, KRZYSZTOF KLOSIN, CRIS POOR, JERRY SHURMAN , and DAVID S. YUEN. Deformations of Saito-Kurokawa type and the Paramodular Conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1821 BERNDTSSON
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Central Limit Theorems for the Real Zeros of Weyl Polynomials Am. J. Math. (IF 1.711) Pub Date : 2020-09-03 Yen Do; Van Vu
Abstract: We establish the central limit theorem for the number of real roots of the Weyl polynomial $P_n(x)=\xi_0+\xi_1 x+\cdots+{1\over\sqrt{n!}}\xi_n x^n$, where $\xi_i$ are iid Gaussian random variables. The main ingredients in the proof are new estimates for the correlation functions of the real roots of $P_n$ and a comparison argument exploiting local laws and repulsion properties of these real
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A summation formula for the Rankin-Selberg monoid and a nonabelian trace formula Am. J. Math. (IF 1.711) Pub Date : 2020-09-03 Jayce R. Getz
Abstract: Let $F$ be a number field and let $\Bbb{A}_F$ be its ring of adeles. Let $B$ be a quaternion algebra over $F$ and let $\nu:B\to F$ be the reduced norm. Consider the reductive monoid $M$ over $F$ whose points in an $F$-algebra $R$ are given by $$ M(R):=\big\{\big(\gamma_1,\gamma_2\big)\in\big(B\otimes_F R\big)^2:\nu\big(\gamma_1\big)=\nu\big(\gamma_2\big)\big\}. $$ Motivated by an influential
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The irreducible components of the primal cohomology of the theta divisor of an abelian fivefold Am. J. Math. (IF 1.711) Pub Date : 2020-09-03 Elham Izadi; Jie Wang
Abstract: The primal cohomology $\Bbb{K}_{\Bbb{Q}}$ of the theta divisor $\Theta$ of a principally polarized abelian fivefold (ppav) is the direct sum of its invariant and anti-invariant parts $\Bbb{K}_{\Bbb{Q}}^{+1}$, resp. $\Bbb{K}_{\Bbb{Q}}^{-1}$ under the action of $-1$. For smooth $\Theta$, these have dimension $6$ and $72$ respectively. We show that $\Bbb{K}_{\Bbb{Q}}^{+1}$ consists of Hodge
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Sign-changing self-similar solutions of the nonlinear heat equation with positive initial value Am. J. Math. (IF 1.711) Pub Date : 2020-09-03 Thierry Cazenave; Flávio Dickstein; Ivan Naumkin; Fred B. Weissler
Abstract: We consider the nonlinear heat equation $u_t-\Delta u=|u|^\alpha u$ on $\Bbb{R}^N$, where $\alpha>0$ and $N\ge 1$. We prove that in the range $0<\alpha<{4\over {N-2}}$, for every $\mu>0$, there exist infinitely many sign-changing, self-similar solutions to the Cauchy problem with initial value $u_0(x)=\mu|x|^{-{2\over\alpha}}$. The construction is based on the analysis of the related inverted
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Global center stable manifold for the defocusing energy critical wave equation with potential Am. J. Math. (IF 1.711) Pub Date : 2020-09-03 Hao Jia; Baoping Liu; Wilhelm Schlag; Guixiang Xu
Abstract: In this paper we consider the defocusing energy critical wave equation with a trapping potential in dimension $3$. We prove that the set of initial data for which solutions scatter to an unstable excited state $(\phi,0)$ forms a finite co-dimensional path connected $C^1$ manifold in the energy space. This manifold is a global and unique center-stable manifold associated with $(\phi,0)$. It
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Rigidity for the spectral gap on Rcd(K, ∞)-spaces Am. J. Math. (IF 1.711) Pub Date : 2020-09-03 Nicola Gigli; Christian Ketterer; Kazumasa Kuwada; Shin-Ichi Ohta
Abstract: We consider a rigidity problem for the spectral gap of the Laplacian on an ${\rm RCD}(K,\infty)$-space (a metric measure space satisfying the Riemannian curvature-dimension condition) for positive $K$. For a weighted Riemannian manifold, Cheng-Zhou showed that the sharp spectral gap is achieved only when a $1$-dimensional Gaussian space is split off. This can be regarded as an infinite-dimensional
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Generic Newton polygon for exponential sums in n variables with parallelotope base Am. J. Math. (IF 1.711) Pub Date : 2020-09-03 Rufei Ren
Abstract: Let $p$ be a prime number. Every $n$-variable polynomial $f(\underline{x})$ over a finite field of characteristic $p$ defines an Artin-Schreier-Witt tower of varieties whose Galois group is isomorphic to $\Bbb{Z}_p$. Our goal of this paper is to study the Newton polygon of the $L$-function associated to a nontrivial finite character of $\Bbb{Z}_p$ and a generic polynomial whose convex hull
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Quotients of triangulated categories and Equivalences of Buchweitz, Orlov, and Amiot-Guo-Keller Am. J. Math. (IF 1.711) Pub Date : 2020-09-03 Osamu Iyama; Dong Yang
Abstract: We give a simple sufficient condition for a Verdier quotient $\scr{T}/\scr{S}$ of a triangulated category $\scr{T}$ by a thick subcategory $\scr{S}$ to be realized inside of $\scr{T}$ as an ideal quotient. As applications, we deduce three significant results by Buchweitz, Orlov and Amiot-Guo-Keller.
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$p$-adic generalized hypergeometric equations from the viewpoint of arithmetic $\scr{D}$-modules}$ Am. J. Math. (IF 1.711) Pub Date : 2020-07-14 Kazuaki Miyatani
abstract: We study the $p$-adic (generalized) hypergeometric equations by using the theory of multiplicative convolution of arithmetic $\scr{D}$-modules. As a result, we prove that the hypergeometric isocrystals with suitable rational parameters have a structure of overconvergent $F$-isocrystals.
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One-Cycle Sweepout Estimates of Essential Surfaces in Closed Riemannian Manifolds Am. J. Math. (IF 1.711) Pub Date : 2020-07-14 Stéphane Sabourau
abstract: We present new free-curvature one-cycle sweepout estimates in Riemannian geometry, both on surfaces and in higher dimension. More precisely, we derive upper bounds on the length of one-parameter families of one-cycles sweeping out essential surfaces in closed Riemannian manifolds. In particular, we show that there exists a homotopically substantial one-cycle sweepout of the essential sphere
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Improvement of Flatness for Nonlocal Phase Transitions Am. J. Math. (IF 1.711) Pub Date : 2020-07-14 Serena Dipierro; Joaquim Serra; Enrico Valdinoci
abstract: We establish an improvement of flatness result for critical points of Ginzburg-Landau energies with long-range interactions. It applies in particular to solutions of $(-\Delta)^{s/2}u=u-u^3$ in $\Bbb{R}^n$ with $s\in(0,1)$. As a corollary, we establish that solutions with asymptotically flat level sets are $1$D and prove the analogue of the De Giorgi conjecture (in the setting of minimizers)
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Fundamental Gap of Convex Domains in the Spheres Am. J. Math. (IF 1.711) Pub Date : 2020-07-14 Chenxu He; Guofang Wei; Qi S. Zhang
abstract: S. Seto, L. Wang, and G. Wei proved that the gap between the first two Dirichlet eigenvalues of a convex domain in the unit sphere is at least as large as that for an associated operator on an interval with the same diameter, provided that the domain has the diameter at most $\pi/2$. In this paper, we extend Seto-Wang-Wei's result to convex domains in the unit sphere with diameter less than
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On a Conjecture of Igusa in Two Dimensions Am. J. Math. (IF 1.711) Pub Date : 2020-07-14 James Wright
abstract: We extend work of Denef and Sperber and also Cluckers regarding a conjecture of Igusa in the two dimensional setting by no longer requiring the polynomial to be nondegenerate with respect to its Newton diagram. More precisely we establish sharp, uniform bounds for complete exponential sums and the number of polynomial congruences for general quasi-homogeneous polynomials in two variables
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Finite Group Actions on Reductive Groups and Buildings and Tamely-Ramified Descent in Bruhat-Tits Theory Am. J. Math. (IF 1.711) Pub Date : 2020-07-14 Gopal Prasad
abstract: Let $K$ be a discretely valued field with Henselian valuation ring and separably closed (but not necessarily perfect) residue field of characteristic $p$, $H$ a connected reductive $K$-group, and $\Theta$ a finite group of automorphisms of $H$. We assume that $p$ does not divide the order of $\Theta$ and Bruhat-Tits theory is available for $H$ over $K$ with $\scr{B}(H/K)$ the Bruhat-Tits
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Sharp Nonexistence Results for Curvature Equations with Four Singular Sources on Rectangular Tori Am. J. Math. (IF 1.711) Pub Date : 2020-07-14 Zhijie Chen; Chang-Shou Lin
abstract: In this paper, we prove that there are no solutions for the curvature equation $$ \Delta u+e^u=8\pi n\delta_0\ {\rm on}\ E_{\tau},\quad n\in\Bbb{N}, $$ where $E_{\tau}$ is a flat rectangular torus and $\delta_0$ is the Dirac measure at the lattice points. This confirms a conjecture of Lin and Wang and also improves a result of Eremenko and Gabrielov. The nonexistence is a delicate problem
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Quantitative Estimates of Sampling Constants in Model Spaces Am. J. Math. (IF 1.711) Pub Date : 2020-07-14 A. Hartmann; P. Jaming; K. Kellay
abstract: We establish quantitative estimates for sampling (dominating) sets in model spaces associated with meromorphic inner functions, i.e., those corresponding to de Branges spaces. Our results encompass the Logvinenko-Sereda-Panejah (LSP) Theorem including Kovrijkine's optimal sampling constants for Paley-Wiener spaces. It also extends Dyakonov's LSP theorem for model spaces associated with bounded
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