发布求助
文献互助 智能选刊 最新文献

American Journal of Mathematics最新文献

筛选
英文 中文
Microlocal decoupling inequalities and the distance problem on Riemannian manifolds 黎曼流形上的微局部解耦不等式与距离问题
IF 1.7 1区 数学
American Journal of Mathematics Pub Date : 2019-09-11 DOI: 10.1353/ajm.2022.0039
A. Iosevich, Bochen Liu, Yakun Xi
{"title":"Microlocal decoupling inequalities and the distance problem on Riemannian manifolds","authors":"A. Iosevich, Bochen Liu, Yakun Xi","doi":"10.1353/ajm.2022.0039","DOIUrl":"https://doi.org/10.1353/ajm.2022.0039","url":null,"abstract":"abstract:We study the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the result of Guth--Iosevich--Ou--Wang for the distance set in the plane to general Riemannian surfaces. Key new ingredients include a family of refined microlocal decoupling inequalities, which are related to the work of Beltran--Hickman--Sogge on Wolff-type inequalities, and an analog of Orponen's radial projection lemma which has proved quite useful in recent work on distance sets.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":"144 1","pages":"1601 - 1639"},"PeriodicalIF":1.7,"publicationDate":"2019-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42530950","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: 8
Noncommutative tensor triangular geometry 非交换张量三角形几何
IF 1.7 1区 数学
American Journal of Mathematics Pub Date : 2019-09-10 DOI: 10.1353/ajm.2022.0041
D. Nakano, Kent B. Vashaw, M. Yakimov
{"title":"Noncommutative tensor triangular geometry","authors":"D. Nakano, Kent B. Vashaw, M. Yakimov","doi":"10.1353/ajm.2022.0041","DOIUrl":"https://doi.org/10.1353/ajm.2022.0041","url":null,"abstract":"abstract:We develop a general noncommutative version of Balmer's tensor triangular geometry that is applicable to arbitrary monoidal triangulated categories (M$Delta$Cs). Insight from noncommutative ring theory is used to obtain a framework for prime, semiprime, and completely prime (thick) ideals of an M$Delta$C, ${bf K}$, and then to associate to ${bf K}$ a topological space--the Balmer spectrum ${rm Spc}{bf K}$. We develop a general framework for (noncommutative) support data, coming in three different flavors, and show that ${rm Spc}{bf K}$ is a universal terminal object for the first two notions (support and weak support). The first two types of support data are then used in a theorem that gives a method for the explicit classification of the thick (two-sided) ideals and the Balmer spectrum of an M$Delta$C. The third type (quasi support) is used in another theorem that provides a method for the explicit classification of the thick right ideals of ${bf K}$, which in turn can be applied to classify the thick two-sided ideals and ${rm Spc}{bf K}$.As a special case, our approach can be applied to the stable module categories of arbitrary finite dimensional Hopf algebras that are not necessarily cocommutative (or quasitriangular). We illustrate the general theorems with classifications of the Balmer spectra and thick two-sided/right ideals for the stable module categories of all small quantum groups for Borel subalgebras, and classifications of the Balmer spectra and thick two-sided ideals of Hopf algebras studied by Benson and Witherspoon.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":"144 1","pages":"1681 - 1724"},"PeriodicalIF":1.7,"publicationDate":"2019-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48118546","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: 10
Circle patterns on surfaces of finite topological type 有限拓扑型曲面上的圆模式
IF 1.7 1区 数学
American Journal of Mathematics Pub Date : 2019-09-08 DOI: 10.2140/pjm.2020.306.203
Huabin Ge, B. Hua, Ze‐hua Zhou
{"title":"Circle patterns on surfaces of finite topological type","authors":"Huabin Ge, B. Hua, Ze‐hua Zhou","doi":"10.2140/pjm.2020.306.203","DOIUrl":"https://doi.org/10.2140/pjm.2020.306.203","url":null,"abstract":"Abstract:This paper investigates circle patterns with obtuse exterior intersection angles on surfaces of finite topological type. We characterise the images of the curvature maps and establish several equivalent conditions regarding long time behaviors of Chow-Luo's combinatorial Ricci flows for these patterns. As consequences, several generalizations of circle pattern theorem are obtained. Moreover, our approach suggests a computational method to find the desired circle patterns.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":"143 1","pages":"1397 - 1430"},"PeriodicalIF":1.7,"publicationDate":"2019-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/pjm.2020.306.203","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47712611","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: 8
Erratum to: Fujita's conjecture and Frobenius amplitude Fujita猜想与Frobenius振幅的勘误表
IF 1.7 1区 数学
American Journal of Mathematics Pub Date : 2019-09-06 DOI: 10.1353/ajm.2019.0039
D. Keeler
{"title":"Erratum to: Fujita's conjecture and Frobenius amplitude","authors":"D. Keeler","doi":"10.1353/ajm.2019.0039","DOIUrl":"https://doi.org/10.1353/ajm.2019.0039","url":null,"abstract":"abstract:We correct [D. S. Keeler, Fujita's conjecture and Frobenius amplitude, Amer. J. Math. {bf 130} (2008), no. 5, 1327--1336].","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":"141 1","pages":"1477 - 1478"},"PeriodicalIF":1.7,"publicationDate":"2019-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1353/ajm.2019.0039","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41664047","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: 3
Cancellation in the additive twists of Fourier coefficients for GL2 and GL3 over number fields GL2和GL3的傅立叶系数在数域上的加性扭曲抵消
IF 1.7 1区 数学
American Journal of Mathematics Pub Date : 2019-09-06 DOI: 10.1353/ajm.2019.0034
Zhi Qi
{"title":"Cancellation in the additive twists of Fourier coefficients for GL2 and GL3 over number fields","authors":"Zhi Qi","doi":"10.1353/ajm.2019.0034","DOIUrl":"https://doi.org/10.1353/ajm.2019.0034","url":null,"abstract":"abstract:In this article, we study the sum of additively twisted Fourier coefficients of an irreducible cuspidal automorphic representation of ${rm GL}_2$ or ${rm GL}_3$ over an arbitrary number field. When the representation is unramified at all non-archimedean places, we prove the Wilton type bound for ${rm GL}_2$ and the Miller type bound for ${rm GL}_3$ which are uniform in terms of the additive character.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":"141 1","pages":"1317 - 1345"},"PeriodicalIF":1.7,"publicationDate":"2019-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1353/ajm.2019.0034","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45876879","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: 10
Existence of minimal hypersurfaces with non-empty free Boundary for generic metrics 一般度量的非空自由边界极小超曲面的存在性
IF 1.7 1区 数学
American Journal of Mathematics Pub Date : 2019-09-04 DOI: 10.1353/ajm.2022.0012
Zhichao Wang
{"title":"Existence of minimal hypersurfaces with non-empty free Boundary for generic metrics","authors":"Zhichao Wang","doi":"10.1353/ajm.2022.0012","DOIUrl":"https://doi.org/10.1353/ajm.2022.0012","url":null,"abstract":"abstract:For almost all Riemannian metrics (in the $C^infty$ Baire sense) on a compact manifold with boundary $(M^{n+1},breakpartial M)$, $3leq (n+1)leq 7$, we prove that, for any open subset $V$ of $partial M$, there exists a compact, properly embedded free boundary minimal hypersurface intersecting $V$.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":"144 1","pages":"599 - 606"},"PeriodicalIF":1.7,"publicationDate":"2019-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44915975","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: 2
Law of large numbers for the spectral radius of random matrix products 随机矩阵乘积谱半径的大数定律
IF 1.7 1区 数学
American Journal of Mathematics Pub Date : 2019-08-20 DOI: 10.1353/AJM.2021.0025
Richard Aoun, Cagri Sert
{"title":"Law of large numbers for the spectral radius of random matrix products","authors":"Richard Aoun, Cagri Sert","doi":"10.1353/AJM.2021.0025","DOIUrl":"https://doi.org/10.1353/AJM.2021.0025","url":null,"abstract":"abstract:We prove that the spectral radius of an i.i.d. random walk on ${rm GL}_d(Bbb{C})$ satisfies a strong law of large numbers under finite second moment assumption and a weak law of large numbers under finite first moment. No irreducibility assumption is supposed.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":"143 1","pages":"1010 - 995"},"PeriodicalIF":1.7,"publicationDate":"2019-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1353/AJM.2021.0025","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44503386","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: 10
Improved bounds for the Kakeya maximal conjecture in higher dimensions 高维Kakeya极大猜想的改进界
IF 1.7 1区 数学
American Journal of Mathematics Pub Date : 2019-08-14 DOI: 10.1353/ajm.2022.0037
J. Hickman, K. Rogers, Ruixiang Zhang
{"title":"Improved bounds for the Kakeya maximal conjecture in higher dimensions","authors":"J. Hickman, K. Rogers, Ruixiang Zhang","doi":"10.1353/ajm.2022.0037","DOIUrl":"https://doi.org/10.1353/ajm.2022.0037","url":null,"abstract":"abstract:We adapt Guth's polynomial partitioning argument for the Fourier restriction problem to the context of the Kakeya problem. By writing out the induction argument as a recursive algorithm, additional multiscale geometric information is made available. To take advantage of this, we prove that direction-separated tubes satisfy a multiscale version of the polynomial Wolff axioms. Altogether, this yields improved bounds for the Kakeya maximal conjecture in~$Bbb{R}^n$ with $n=5$ or $nge 7$ and improved bounds for the Kakeya set conjecture for an infinite sequence of dimensions.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":"144 1","pages":"1511 - 1560"},"PeriodicalIF":1.7,"publicationDate":"2019-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46979672","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: 17
Structure and classification results for the ∞-elastica problem ∞弹性问题的结构与分类结果
IF 1.7 1区 数学
American Journal of Mathematics Pub Date : 2019-08-05 DOI: 10.1353/ajm.2022.0030
R. Moser
{"title":"Structure and classification results for the ∞-elastica problem","authors":"R. Moser","doi":"10.1353/ajm.2022.0030","DOIUrl":"https://doi.org/10.1353/ajm.2022.0030","url":null,"abstract":"abstract:We consider the following variational problem: among all curves in $Bbb{R}^n$ of fixed length with prescribed end points and prescribed tangents at the end points, minimise the $L^infty$-norm of the curvature. We show that the solutions of this problem, and of a generalised version, are characterised by a system of differential equations. Furthermore, we have a lot of information about the structure of solutions, which allows a classification.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":"144 1","pages":"1299 - 1329"},"PeriodicalIF":1.7,"publicationDate":"2019-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48233152","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: 6
Dimension-Free Estimates for Discrete Hardy-Littlewood Averaging Operators Over the Cubes in ℤd 中立方体上离散Hardy-Littlewood平均算子的无量纲估计ℤd
IF 1.7 1区 数学
American Journal of Mathematics Pub Date : 2019-07-24 DOI: 10.1353/ajm.2019.0023
J. Bourgain, Mariusz Mirek, E. Stein, B. Wróbel
{"title":"Dimension-Free Estimates for Discrete Hardy-Littlewood Averaging Operators Over the Cubes in ℤd","authors":"J. Bourgain, Mariusz Mirek, E. Stein, B. Wróbel","doi":"10.1353/ajm.2019.0023","DOIUrl":"https://doi.org/10.1353/ajm.2019.0023","url":null,"abstract":"abstract:Dimension-free bounds will be provided in maximal and $r$-variational inequalities on $ell^p({Bbb Z}^d)$ corresponding to the discrete Hardy-Littlewood averaging operators defined over the cubes in ${Bbb Z}^d$. We will also construct an example of a symmetric convex body in ${Bbb Z}^d$ for which maximal dimension-free bounds fail on $ell^p({Bbb Z}^d)$ for all $pin(1,infty)$. Finally, some applications in ergodic theory will be discussed.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":"141 1","pages":"587 - 905"},"PeriodicalIF":1.7,"publicationDate":"2019-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1353/ajm.2019.0023","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48156591","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: 15
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：604180095
Book学术官方微信