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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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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
The Dirichlet problem for the k-Hessian equation on a complex manifold 复流形上k-Hessian方程的Dirichlet问题
IF 1.7 1区 数学
American Journal of Mathematics Pub Date : 2019-09-01 DOI: 10.1353/ajm.2022.0040
Tristan C. Collins, Sebastien Picard
{"title":"The Dirichlet problem for the k-Hessian equation on a complex manifold","authors":"Tristan C. Collins, Sebastien Picard","doi":"10.1353/ajm.2022.0040","DOIUrl":"https://doi.org/10.1353/ajm.2022.0040","url":null,"abstract":"abstract:We solve the Dirichlet problem for $k$-Hessian equations on compact complex manifolds with boundary, given the existence of a subsolution. Our method is based on a second order a priori estimate of the solution on the boundary with a particular gradient scale. The scale allows us to apply a blow-up argument to obtain control on all necessary norms of the solution.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42115387","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
Rigid surfaces arbitrarily close to the Bogomolov–Miyaoka–Yau line 刚性表面任意接近Bogomolov-Miyaoka-Yau线
IF 1.7 1区 数学
American Journal of Mathematics Pub Date : 2019-09-01 DOI: 10.1353/ajm.2022.0044
Matthew Stover, G. Urz'ua
{"title":"Rigid surfaces arbitrarily close to the Bogomolov–Miyaoka–Yau line","authors":"Matthew Stover, G. Urz'ua","doi":"10.1353/ajm.2022.0044","DOIUrl":"https://doi.org/10.1353/ajm.2022.0044","url":null,"abstract":"abstract:We prove the existence of rigid compact complex surfaces of general type whose Chern slopes are arbitrarily close to the Bogomolov--Miyaoka--Yau bound of $3$. In addition, each of these surfaces has first Betti number equal to $4$.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48868305","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":null,"pages":null},"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":null,"pages":null},"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
On Arthur's unitarity conjecture for split real groups 论分裂实数群的Arthur的单一性猜想
IF 1.7 1区 数学
American Journal of Mathematics Pub Date : 2019-08-12 DOI: 10.1353/ajm.2022.0038
Joseph Hundley, S. Miller
{"title":"On Arthur's unitarity conjecture for split real groups","authors":"Joseph Hundley, S. Miller","doi":"10.1353/ajm.2022.0038","DOIUrl":"https://doi.org/10.1353/ajm.2022.0038","url":null,"abstract":"abstract:Arthur's conjectures predict the existence of some very interesting unitary representations occurring in spaces of automorphic forms. We prove the unitarity of the ``Langlands element'' (i.e., the representation specified by Arthur) of all unipotent Arthur packets for split real exceptional groups. The proof uses Eisenstein series, Langlands' constant term formula and square integrability criterion, analytic properties of intertwining operators, and some mild arithmetic input from the theory of Dirichlet $L$-functions, to reduce to a more combinatorial problem about intertwining operators.","PeriodicalId":7453,"journal":{"name":"American Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2019-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45163971","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: 1
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":null,"pages":null},"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
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