Communications on Pure and Applied Mathematics最新文献

英文中文

A priori bounds for the generalised parabolic Anderson model 广义抛物型Anderson模型的先验界

IF 3 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics

Pub Date : 2026-01-12 DOI: 10.1002/cpa.70025

Ajay Chandra, Guilherme de Lima Feltes, Hendrik Weber

We show a priori bounds for solutions to in finite volume in the framework of Hairer's Regularity Structures [Invent Math 198:269–504, 2014]. We assume and that is of negative Hölder regularity of order where for an explicit , and that it can be lifted to a model in the sense of Regularity Structures. Our main results guarantee non‐explosion of the solution in finite time and a growth, which is at most polynomial in . Our estimates imply global well‐posedness for the 2‐d generalised parabolic Anderson model on the torus, as well as for the parabolic quantisation of the Sine–Gordon Euclidean quantum fieldtheory (EQFT) on the torus in the regime . We also consider the parabolic quantisation of a massive Sine–Gordon EQFT and derive estimates that imply the existence of the measure for the same range of . Finally, our estimates apply to Itô SPDEs in the sense of Da Prato‐Zabczyk [ Stochastic Equations in Infinite Dimensions , Enc. Math. App., Cambridge Univ. Press, 1992] and imply existence of a stochastic flow beyond the trace‐class regime.

我们在有限体积的Hairer正则结构框架下给出了一个先验边界[发明数学198:269-504,2014]。我们假设，这是负的Hölder规则的秩序，其中一个明确的，它可以提升到一个模型的意义上的规则结构。我们的主要结果保证了解在有限时间内的非爆炸性，并保证了一个最多为多项式的增长。我们的估计意味着环面上的二维广义抛物型安德森模型的全局适定性，以及环面上的正弦-戈登欧几里德量子场论（EQFT）的抛物量子化。我们还考虑了一个巨大的正弦-戈登EQFT的抛物量化，并推导了在相同范围内存在度量的估计。最后，我们的估计适用于Da Prato‐Zabczyk[无限维随机方程，数学等]意义上的Itô spde。App.，剑桥大学出版社，1992]，并暗示了一种超越迹级状态的随机流的存在。

引用次数: 0

Eventual regularization of fractional mean curvature flow 分数平均曲率流的最终正则化

IF 3 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics

Pub Date : 2026-01-12 DOI: 10.1002/cpa.70028

Stephen Cameron

We show that any open set that is a finite distance away from a Lipschitz subgraph will become a Lipschitz subgraph after flowing under fractional mean curvature flow for a finite, universal time. Our proof is quantitative and inherently nonlocal, as the corresponding statement is false for classical mean curvature flow. This is the first regularizing effect proven for weak solutions to nonlocal curvature flow.

我们证明了任何距离Lipschitz子图有有限距离的开集，在有限的普适时间内，在分数平均曲率下流动后，将成为Lipschitz子图。我们的证明是定量的，本质上是非局部的，因为相应的陈述对经典平均曲率流是错误的。这是首次证明了非局部曲率流弱解的正则化效应。

引用次数: 0

3‐Manifolds With Positive Scalar Curvature and Bounded Geometry 具有正标量曲率和有界几何的流形

IF 3 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics

Pub Date : 2026-01-08 DOI: 10.1002/cpa.70029

Otis Chodosh, Yi Lai, Kai Xu

We show that a complete contractible 3‐manifold with positive scalar curvature and bounded geometry must be . We also show that an open handlebody of genus larger than 1 does not admit complete metrics with positive scalar curvature and bounded geometry. Our results rely on the maximal weak solution to inverse mean curvature flow due to the third‐named author.

我们证明了具有正标量曲率和有界几何的完全可收缩3 -流形必须是。我们还证明了一个大于1的开柄体不允许具有正标量曲率和有界几何的完全度量。我们的结果依赖于由第三名作者提出的逆平均曲率流的最大弱解。

引用次数: 0

Degree theory for 4‐dimensional asymptotically conical gradient expanding solitons 四维渐近圆锥梯度展开孤子的度理论

IF 3 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics

Pub Date : 2025-12-16 DOI: 10.1002/cpa.70024

Richard H. Bamler, Eric Chen

We develop a new degree theory for 4‐dimensional, asymptotically conical gradient expanding solitons. Our theory implies the existence of gradient expanding solitons that are asymptotic to any given cone over with non‐negative scalar curvature. We also obtain a similar existence result for cones whose link is diffeomorphic to if we allow the expanding soliton to have orbifold singularities. Our theory reveals the existence of a new topological invariant, called the expander degree , applicable to a particular class of compact, smooth 4‐orbifolds with boundary. This invariant is roughly equal to a signed count of all possible gradient expanding solitons that can be defined on the interior of the orbifold and are asymptotic to any fixed cone metric with non‐negative scalar curvature. If the expander degree of an orbifold is non‐zero, then gradient expanding solitons exist for any such cone metric. We show that the expander degree of the 4‐disk and any orbifold of the form equals 1. Additionally, we demonstrate that the expander degree of certain orbifolds, including exotic 4‐disks, vanishes. Our theory also sheds light on the relation between gradient and non‐gradient expanding solitons with respect to their asymptotic model. More specifically, we show that among the set of asymptotically conical expanding solitons, the subset of those solitons that are gradient forms a union of connected components.

我们发展了一个新的四维渐近圆锥梯度展开孤子的度理论。我们的理论暗示了梯度膨胀孤子的存在性，这些孤子对任意给定的非负标量曲率的圆锥渐近。如果允许膨胀孤子具有轨道奇异性，我们也得到了连杆为微分同态的锥的类似存在性结果。我们的理论揭示了一个新的拓扑不变量的存在性，称为扩展度，适用于一类特定的紧的，光滑的具有边界的4‐轨道。这个不变量大致等于所有可能的梯度展开孤子的带符号计数，这些孤子可以定义在轨道的内部，并且渐近于任何具有非负标量曲率的固定锥度规。如果一个轨道的展开度是非零的，那么对于任何这样的圆锥度规都存在梯度展开孤子。我们证明了4 -盘和任何形式的轨道的膨胀度等于1。此外，我们证明了某些轨道的膨胀度，包括奇异的4 -盘，会消失。我们的理论还揭示了梯度和非梯度膨胀孤子的渐近模型之间的关系。更具体地说，我们证明了在渐近圆锥展开孤子集合中，这些梯度孤子的子集构成了连通分量的并集。

{"title":"Degree theory for 4‐dimensional asymptotically conical gradient expanding solitons","authors":"Richard H. Bamler, Eric Chen","doi":"10.1002/cpa.70024","DOIUrl":"https://doi.org/10.1002/cpa.70024","url":null,"abstract":"We develop a new degree theory for 4‐dimensional, asymptotically conical gradient expanding solitons. Our theory implies the existence of gradient expanding solitons that are asymptotic to any given cone over with non‐negative scalar curvature. We also obtain a similar existence result for cones whose link is diffeomorphic to if we allow the expanding soliton to have orbifold singularities. Our theory reveals the existence of a new topological invariant, called the expander degree , applicable to a particular class of compact, smooth 4‐orbifolds with boundary. This invariant is roughly equal to a signed count of all possible gradient expanding solitons that can be defined on the interior of the orbifold and are asymptotic to any fixed cone metric with non‐negative scalar curvature. If the expander degree of an orbifold is non‐zero, then gradient expanding solitons exist for any such cone metric. We show that the expander degree of the 4‐disk and any orbifold of the form equals 1. Additionally, we demonstrate that the expander degree of certain orbifolds, including exotic 4‐disks, vanishes. Our theory also sheds light on the relation between gradient and non‐gradient expanding solitons with respect to their asymptotic model. More specifically, we show that among the set of asymptotically conical expanding solitons, the subset of those solitons that are gradient forms a union of connected components.","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"66 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145759574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Weighted extremal kähler metrics on resolutions of singularities 奇异点分辨率的加权极值kähler度量

IF 2.7 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics

Pub Date : 2025-12-05 DOI: 10.1002/cpa.70026

Sébastien Boucksom, Mattias Jonsson, Antonio Trusiani

Generalizing previous results of Arezzo–Pacard–Singer, Seyyedali–Székelyhidi, and Hallam, we prove the invariance under smooth blowups of the class of weighted extremal Kähler manifolds, modulo a log-concavity assumption on the first weight. Through recent work of Di Nezza–Jubert–Lahdili and Han–Liu, this is obtained as a consequence of a general uniform coercivity estimate for the (relative, weighted) Mabuchi energy on the blowup, which applies more generally to any equivariant resolution of singularities of Fano type of a compact Kähler klt space whose Mabuchi energy is assumed to be coercive.

推广了Arezzo-Pacard-Singer， seyyedali - sz kelyhidi， and Hallam之前的结果，证明了一类加权极值Kähler流形在光滑膨胀下的不变性，在第一权值上取对数凹性的模。通过Di Nezza-Jubert-Lahdili和Han-Liu最近的工作，这是作为（相对的，加权的）Mabuchi能量在blowup上的一般均匀矫顽力估计的结果得到的，它更普遍地适用于紧化Kähler klt空间的Fano型奇点的任何等变分辨率，其中Mabuchi能量被假设为矫顽力。

引用次数: 0

Isoperimetric inequalities on slabs with applications to cubes and Gaussian slabs 平板上的等周不等式及其在立方体和高斯平板上的应用

IF 2.7 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics

Pub Date : 2025-11-27 DOI: 10.1002/cpa.70020

Emanuel Milman

We study isoperimetric inequalities on “slabs”, namely weighted Riemannian manifolds obtained as the product of the uniform measure on a finite length interval with a codimension-one base. As our two main applications, we consider the case when the base is the flat torus <math> <semantics> <mrow> <msup> <mi>R</mi> <mn>2</mn> </msup> <mo>/</mo> <mn>2</mn> <msup> <mi>Z</mi> <mn>2</mn> </msup> </mrow> <annotation>$mathbb {R}^2 / 2 mathbb {Z}^2$</annotation> </semantics></math> and the standard Gaussian measure on <math> <semantics> <msup> <mi>R</mi> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> <annotation>$mathbb {R}^{n-1}$</annotation> </semantics></math>. The isoperimetric conjecture on the three-dimensional cube predicts that minimizers are enclosed by spheres about a corner, cylinders about an edge and coordinate planes. This has only been established for relative volumes close to 0, <math> <semantics> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> <annotation>$1/2$</annotation> </semantics></math> and 1 by compactness arguments. Our analysis confirms the isoperimetric conjecture on the three-dimensional cube with side lengths <math> <semantics> <mrow> <mo>(</mo> <mi>β</mi> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> <annotation>$(beta,1,1)$</annotation> </semantics></math> in a new range of relative volumes <math> <semantics> <mrow> <mover> <mi>v</mi> <mo>¯</mo> </mover> <mo>∈</mo> <mrow> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>]</mo> </mrow> </mrow> <annotation>$bar{v} in [0,1/2]$</annotation> </semantics></math>. In particular, we co

我们研究了“平板”上的等周不等式，即加权黎曼流形，它是余维为1基的有限长度区间上的一致测度的乘积。作为我们的两个主要应用，我们考虑了基底是平面环面和标准高斯测度的情况。三维立方体上的等周猜想预言，最小值被围绕一个角的球体、围绕一个边的圆柱体和坐标平面所包围。这只适用于相对体积接近0和紧凑性参数接近1的情况。我们的分析证实了边长在一个新的相对体积范围内的三维立方体的等周猜想。特别地，我们确认了所有的标准立方体（）的猜想，当整个范围内的球体被推测为最小，也为所有。当我们将全猜想的有效性降低到建立半平面是等周最小化时。我们还证明了高维立方体上的类似猜想是假的。对于宽度为高斯基底的板，我们在何时和何时确定相变。特别地，当与的半平面积总是最小时，当它们永远不会最小时，被高斯不流击败。在这个范围内，可能发生三分术。

{"title":"Isoperimetric inequalities on slabs with applications to cubes and Gaussian slabs","authors":"Emanuel Milman","doi":"10.1002/cpa.70020","DOIUrl":"10.1002/cpa.70020","url":null,"abstract":"We study isoperimetric inequalities on “slabs”, namely weighted Riemannian manifolds obtained as the product of the uniform measure on a finite length interval with a codimension-one base. As our two main applications, we consider the case when the base is the flat torus <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mo>/</mo>\u0000 <mn>2</mn>\u0000 <msup>\u0000 <mi>Z</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$mathbb {R}^2 / 2 mathbb {Z}^2$</annotation>\u0000 </semantics></math> and the standard Gaussian measure on <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$mathbb {R}^{n-1}$</annotation>\u0000 </semantics></math>. The isoperimetric conjecture on the three-dimensional cube predicts that minimizers are enclosed by spheres about a corner, cylinders about an edge and coordinate planes. This has only been established for relative volumes close to 0, <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>/</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$1/2$</annotation>\u0000 </semantics></math> and 1 by compactness arguments. Our analysis confirms the isoperimetric conjecture on the three-dimensional cube with side lengths <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>β</mi>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(beta,1,1)$</annotation>\u0000 </semantics></math> in a new range of relative volumes <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mover>\u0000 <mi>v</mi>\u0000 <mo>¯</mo>\u0000 </mover>\u0000 <mo>∈</mo>\u0000 <mrow>\u0000 <mo>[</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>/</mo>\u0000 <mn>2</mn>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$bar{v} in [0,1/2]$</annotation>\u0000 </semantics></math>. In particular, we co","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"79 4","pages":"1012-1072"},"PeriodicalIF":2.7,"publicationDate":"2025-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cpa.70020","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145608974","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Mack modes in supersonic boundary layer 超声速边界层Mack模态

IF 2.7 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics

Pub Date : 2025-11-20 DOI: 10.1002/cpa.70022

Nader Masmoudi, Yuxi Wang, Di Wu, Zhifei Zhang

Understanding the transition mechanism of boundary layer flows is of great significance in physics and engineering, especially due to the current development of supersonic and hypersonic aircraft. In this paper, we construct multiple unstable acoustic modes so-called, Mack modes, which play a crucial role during the early stage of transition in the supersonic boundary layer. To this end, we develop an inner-outer gluing iteration to solve a hyperbolic-elliptic mixed type and singular system.

特别是在超声速和高超声速飞机发展的今天，了解边界层流动的过渡机制在物理和工程上具有重要意义。在本文中，我们构建了多个不稳定的声学模态，即Mack模态，它们在超音速边界层过渡的早期阶段起着至关重要的作用。为此，我们提出了一种内外胶合迭代法来求解双曲椭圆型混合奇异系统。

引用次数: 0

Sharp quantitative stability of the Dirichlet spectrum near the ball 球附近狄利克雷谱的尖锐定量稳定性

IF 2.7 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics

Pub Date : 2025-11-14 DOI: 10.1002/cpa.70021

Dorin Bucur, Jimmy Lamboley, Mickaël Nahon, Raphaël Prunier

Let $� � � Ω � \subset � �^{R � n �} � � �$ be an open set with the same volume as the unit ball $� � B � �$ and let $� � � �_{λ � k �} � � (� Ω �) � � � �$ be the $� � k � �$ -th eigenvalue of the Laplace operator of $� � Ω � �$ with Dirichlet boundary conditions on $� � � \partial � Ω � � �$ . In this work, we answer the following question:

设一个与单位球体积相同的开集，设有狄利克雷边界条件的拉普拉斯算子的第一个特征值。在这项工作中，我们回答了以下问题：如果是小的，可以有多大？我们根据的多重性，建立了具有尖锐指数形式的定量界限。我们首先证明了这样的不等式对于任何都是有效的，改进了以前已知的结果并提供了可能的最尖锐的指数。然后，通过对无向量边界问题的研究，我们证明了如果简单，可以得到较好的指数。当为倍数时，我们对整个特征值簇也得到了类似的结果，从而对上面的问题提供了一个完整的答案。作为这些结果的结果，我们得到了球作为一大类谱泛函的最小值的持续性，这些泛函一方面是基本特征值的小扰动，另一方面是完全逆的Kohler-Jobin不等式，解决了M. Van Den Berg， G. Buttazzo和a . Pratelli提出的开放问题。

{"title":"Sharp quantitative stability of the Dirichlet spectrum near the ball","authors":"Dorin Bucur, Jimmy Lamboley, Mickaël Nahon, Raphaël Prunier","doi":"10.1002/cpa.70021","DOIUrl":"10.1002/cpa.70021","url":null,"abstract":"Let <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Ω</mi>\u0000 <mo>⊂</mo>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$Omega subset mathbb {R}^n$</annotation>\u0000 </semantics></math> be an open set with the same volume as the unit ball <math>\u0000 <semantics>\u0000 <mi>B</mi>\u0000 <annotation>$B$</annotation>\u0000 </semantics></math> and let <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>λ</mi>\u0000 <mi>k</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>Ω</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$lambda _k(Omega)$</annotation>\u0000 </semantics></math> be the <math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math>-th eigenvalue of the Laplace operator of <math>\u0000 <semantics>\u0000 <mi>Ω</mi>\u0000 <annotation>$Omega$</annotation>\u0000 </semantics></math> with Dirichlet boundary conditions on <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>∂</mi>\u0000 <mi>Ω</mi>\u0000 </mrow>\u0000 <annotation>$partial Omega$</annotation>\u0000 </semantics></math>. In this work, we answer the following question: \u0000\u0000 ","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"79 4","pages":"827-896"},"PeriodicalIF":2.7,"publicationDate":"2025-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145509281","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Semiclassical inequalities for Dirichlet and Neumann Laplacians on convex domains 凸域上Dirichlet和Neumann拉普拉斯算子的半经典不等式

IF 2.7 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics

Pub Date : 2025-10-24 DOI: 10.1002/cpa.70019

Rupert L. Frank, Simon Larson

We are interested in inequalities that bound the Riesz means of the eigenvalues of the Dirichlet and Neumann Laplacians in terms of their semiclassical counterpart. We show that the classical inequalities of Berezin–Li–Yau and Kröger, valid for Riesz exponents $� � � γ � \geq � 1 � � �$ , extend to certain values $� � � γ � < � 1 � � �$ , provided the underlying domain is convex. We also study the corresponding optimization problems and describe the implications of a possible failure of Pólya's conjecture for convex sets in terms of Riesz means. These findings allow us to describe the asymptotic behavior of solutions of a spectral shape optimization problem for convex sets.

我们感兴趣的是约束狄利克雷和诺伊曼拉普拉斯特征值的Riesz均值的不等式用它们的半经典对应物表示。我们证明了经典的Berezin-Li-Yau和Kröger不等式，对于Riesz指数有效，扩展到一定的值，假设底层域是凸的。我们还研究了相应的优化问题，并描述了Pólya猜想在凸集上可能失效的Riesz means的含义。这些发现使我们能够描述凸集的谱形状优化问题解的渐近行为。

{"title":"Semiclassical inequalities for Dirichlet and Neumann Laplacians on convex domains","authors":"Rupert L. Frank, Simon Larson","doi":"10.1002/cpa.70019","DOIUrl":"10.1002/cpa.70019","url":null,"abstract":"We are interested in inequalities that bound the Riesz means of the eigenvalues of the Dirichlet and Neumann Laplacians in terms of their semiclassical counterpart. We show that the classical inequalities of Berezin–Li–Yau and Kröger, valid for Riesz exponents <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>γ</mi>\u0000 <mo>≥</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$gamma ge 1$</annotation>\u0000 </semantics></math>, extend to certain values <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>γ</mi>\u0000 <mo><</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$gamma <1$</annotation>\u0000 </semantics></math>, provided the underlying domain is convex. We also study the corresponding optimization problems and describe the implications of a possible failure of Pólya's conjecture for convex sets in terms of Riesz means. These findings allow us to describe the asymptotic behavior of solutions of a spectral shape optimization problem for convex sets.","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"79 3","pages":"762-822"},"PeriodicalIF":2.7,"publicationDate":"2025-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cpa.70019","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145381744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Avila's acceleration via zeros of determinants and applications to Schrödinger cocycles Avila通过零行列式的加速和Schrödinger环的应用

IF 2.7 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics

Pub Date : 2025-10-22 DOI: 10.1002/cpa.70018

Rui Han, Wilhelm Schlag

In this paper we give a characterization of Avila's quantized acceleration of the Lyapunov exponent via the number of zeros of the Dirichlet determinants in finite volume. As applications, we prove $� � β � �$ -Hölder continuity of the integrated density of states for supercritical quasi-periodic Schrödinger operators restricted to the $� � ℓ � �$ th stratum, for any $� � � β � < � �^{� (� 2 � � (� ℓ � - � 1 �) � �) � � � - � 1 � �} � � �$ and $� � � ℓ � \geq � 2 � � �$ . We establish Anderson localization for all Diophantine frequencies for the operator with even analytic potential function on the first supercritical stratum, which has positive measure if it is nonempty.

本文通过有限体积中狄利克雷行列式的零个数，给出了李雅普诺夫指数的Avila量化加速度的表征。作为应用，我们证明了限制于第1层的超临界拟周期Schrödinger算符的态积分密度的‐Hölder连续性。我们建立了第一超临界层上具有偶解析势函数的算子的所有丢芬图频率的Anderson局域化，该算子非空时具有正测度。

{"title":"Avila's acceleration via zeros of determinants and applications to Schrödinger cocycles","authors":"Rui Han, Wilhelm Schlag","doi":"10.1002/cpa.70018","DOIUrl":"10.1002/cpa.70018","url":null,"abstract":"In this paper we give a characterization of Avila's quantized acceleration of the Lyapunov exponent via the number of zeros of the Dirichlet determinants in finite volume. As applications, we prove <math>\u0000 <semantics>\u0000 <mi>β</mi>\u0000 <annotation>$beta$</annotation>\u0000 </semantics></math>-Hölder continuity of the integrated density of states for supercritical quasi-periodic Schrödinger operators restricted to the <math>\u0000 <semantics>\u0000 <mi>ℓ</mi>\u0000 <annotation>$ell$</annotation>\u0000 </semantics></math>th stratum, for any <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>β</mi>\u0000 <mo><</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mn>2</mn>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>ℓ</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$beta <(2(ell -1))^{-1}$</annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ℓ</mi>\u0000 <mo>≥</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$ell ge 2$</annotation>\u0000 </semantics></math>. We establish Anderson localization for all Diophantine frequencies for the operator with even analytic potential function on the first supercritical stratum, which has positive measure if it is nonempty.","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"79 3","pages":"729-761"},"PeriodicalIF":2.7,"publicationDate":"2025-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145396447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

首页上一页

下一页尾页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Communications on Pure and Applied Mathematics

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀