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Analysis and Geometry in Metric Spaces最新文献

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Double Bubbles on the Real Line with Log-Convex Density 对数凸密度实线上的双气泡
IF 1 3区 数学
Analysis and Geometry in Metric Spaces Pub Date : 2017-08-10 DOI: 10.1515/agms-2018-0004
Eliot Bongiovanni, Leonardo Di Giosia, Alejandro Diaz, Jahangir Habib, Arjun Kakkar, Lea Kenigsberg, Dylanger S. Pittman, Nat Sothanaphan, Weitao Zhu
{"title":"Double Bubbles on the Real Line with Log-Convex Density","authors":"Eliot Bongiovanni, Leonardo Di Giosia, Alejandro Diaz, Jahangir Habib, Arjun Kakkar, Lea Kenigsberg, Dylanger S. Pittman, Nat Sothanaphan, Weitao Zhu","doi":"10.1515/agms-2018-0004","DOIUrl":"https://doi.org/10.1515/agms-2018-0004","url":null,"abstract":"Abstract The classic double bubble theorem says that the least-perimeter way to enclose and separate two prescribed volumes in ℝN is the standard double bubble. We seek the optimal double bubble in ℝN with density, which we assume to be strictly log-convex. For N = 1 we show that the solution is sometimes two contiguous intervals and sometimes three contiguous intervals. In higher dimensions we think that the solution is sometimes a standard double bubble and sometimes concentric spheres (e.g. for one volume small and the other large).","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2017-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/agms-2018-0004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49166372","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 5
Products of Snowflaked Euclidean Lines Are Not Minimal for Looking Down 雪花欧氏线的产品不是最小的向下看
IF 1 3区 数学
Analysis and Geometry in Metric Spaces Pub Date : 2017-08-09 DOI: 10.1515/agms-2017-0005
Matthieu Joseph, T. Rajala
{"title":"Products of Snowflaked Euclidean Lines Are Not Minimal for Looking Down","authors":"Matthieu Joseph, T. Rajala","doi":"10.1515/agms-2017-0005","DOIUrl":"https://doi.org/10.1515/agms-2017-0005","url":null,"abstract":"Abstract We show that products of snowflaked Euclidean lines are not minimal for looking down. This question was raised in Fractured fractals and broken dreams, Problem 11.17, by David and Semmes. The proof uses arguments developed by Le Donne, Li and Rajala to prove that the Heisenberg group is not minimal for looking down. By a method of shortcuts, we define a new distance d such that the product of snowflaked Euclidean lines looks down on (RN , d), but not vice versa.","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2017-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/agms-2017-0005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43547029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
An Analog of the Neumann Problem for the 1-Laplace Equation in the Metric Setting: Existence, Boundary Regularity, and Stability 度量条件下1-Laplace方程Neumann问题的一个类比：存在性、边界正则性和稳定性
IF 1 3区 数学
Analysis and Geometry in Metric Spaces Pub Date : 2017-08-08 DOI: 10.1515/agms-2018-0001
P. Lahti, Lukáš Malý, N. Shanmugalingam
{"title":"An Analog of the Neumann Problem for the 1-Laplace Equation in the Metric Setting: Existence, Boundary Regularity, and Stability","authors":"P. Lahti, Lukáš Malý, N. Shanmugalingam","doi":"10.1515/agms-2018-0001","DOIUrl":"https://doi.org/10.1515/agms-2018-0001","url":null,"abstract":"Abstract We study an inhomogeneous Neumann boundary value problem for functions of least gradient on bounded domains in metric spaces that are equipped with a doubling measure and support a Poincaré inequality. We show that solutions exist under certain regularity assumptions on the domain, but are generally nonunique. We also show that solutions can be taken to be differences of two characteristic functions, and that they are regular up to the boundary when the boundary is of positive mean curvature. By regular up to the boundary we mean that if the boundary data is 1 in a neighborhood of a point on the boundary of the domain, then the solution is −1 in the intersection of the domain with a possibly smaller neighborhood of that point. Finally, we consider the stability of solutions with respect to boundary data.","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2017-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/agms-2018-0001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42222917","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 5
Lipschitz Extensions to Finitely Many Points 有限多点的Lipschitz推广
IF 1 3区 数学
Analysis and Geometry in Metric Spaces Pub Date : 2017-07-20 DOI: 10.1515/agms-2018-0010
Giuliano Basso
{"title":"Lipschitz Extensions to Finitely Many Points","authors":"Giuliano Basso","doi":"10.1515/agms-2018-0010","DOIUrl":"https://doi.org/10.1515/agms-2018-0010","url":null,"abstract":"Abstract We consider Lipschitz maps with values in quasi-metric spaces and extend such maps to finitely many points. We prove that in this context every 1-Lipschitz map admits an extension such that its Lipschitz constant is bounded from above by the number of added points plus one. Moreover, we prove that if the source space is a Hilbert space and the target space is a Banach space, then there exists an extension such that its Lipschitz constant is bounded from above by the square root of the total of added points plus one. We discuss applications to metric transforms.","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2017-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/agms-2018-0010","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41575215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 4
Distance Bounds for Graphs with Some Negative Bakry-Émery Curvature 具有负Bakry-Émery曲率的图的距离界
IF 1 3区 数学
Analysis and Geometry in Metric Spaces Pub Date : 2017-05-23 DOI: 10.1515/agms-2019-0001
Shiping Liu, Florentin Münch, N. Peyerimhoff, Christian Rose
{"title":"Distance Bounds for Graphs with Some Negative Bakry-Émery Curvature","authors":"Shiping Liu, Florentin Münch, N. Peyerimhoff, Christian Rose","doi":"10.1515/agms-2019-0001","DOIUrl":"https://doi.org/10.1515/agms-2019-0001","url":null,"abstract":"Abstract We prove distance bounds for graphs possessing positive Bakry-Émery curvature apart from an exceptional set, where the curvature is allowed to be non-positive. If the set of non-positively curved vertices is finite, then the graph admits an explicit upper bound for the diameter. Otherwise, the graph is a subset of the tubular neighborhood with an explicit radius around the non-positively curved vertices. Those results seem to be the first assuming non-constant Bakry-Émery curvature assumptions on graphs.","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2017-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/agms-2019-0001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42848206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 13
Thinnest Covering of the Euclidean Plane with Incongruent Circles 具有不规则圆的欧氏平面的最薄覆盖
IF 1 3区 数学
Analysis and Geometry in Metric Spaces Pub Date : 2017-03-01 DOI: 10.1515/AGMS-2017-0002
D. Dorninger
{"title":"Thinnest Covering of the Euclidean Plane with Incongruent Circles","authors":"D. Dorninger","doi":"10.1515/AGMS-2017-0002","DOIUrl":"https://doi.org/10.1515/AGMS-2017-0002","url":null,"abstract":"Abstract In 1958 L. Fejes Tóth and J. Molnar proposed a conjecture about a lower bound for the thinnest covering of the plane by circles with arbitrary radii from a given interval of the reals. If only two kinds of radii can occur this conjecture was in essence proven by A. Florian in 1962, leaving the general case unanswered till now. The goal of this paper is to analytically describe the general case in such a way that the conjecture can easily be numerically verified and upper and lower limits for the asserted bound can be gained.","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2017-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/AGMS-2017-0002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42236589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Angles between Curves in Metric Measure Spaces 度量空间中曲线间的夹角
IF 1 3区 数学
Analysis and Geometry in Metric Spaces Pub Date : 2017-01-18 DOI: 10.1515/agms-2017-0003
B. Han, A. Mondino
{"title":"Angles between Curves in Metric Measure Spaces","authors":"B. Han, A. Mondino","doi":"10.1515/agms-2017-0003","DOIUrl":"https://doi.org/10.1515/agms-2017-0003","url":null,"abstract":"Abstract The goal of the paper is to study the angle between two curves in the framework of metric (and metric measure) spaces. More precisely, we give a new notion of angle between two curves in a metric space. Such a notion has a natural interplay with optimal transportation and is particularly well suited for metric measure spaces satisfying the curvature-dimension condition. Indeed one of the main results is the validity of the cosine formula on RCD*(K, N) metric measure spaces. As a consequence, the new introduced notions are compatible with the corresponding classical ones for Riemannian manifolds, Ricci limit spaces and Alexandrov spaces.","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2017-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/agms-2017-0003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43679773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Hardy and Hardy-Sobolev Spaces on Strongly Lipschitz Domains and Some Applications 强Lipschitz域上的Hardy和Hardy- sobolev空间及其应用
IF 1 3区 数学
Analysis and Geometry in Metric Spaces Pub Date : 2016-12-30 DOI: 10.1515/agms-2016-0017
Xiaming Chen, Renjin Jiang, Dachun Yang
{"title":"Hardy and Hardy-Sobolev Spaces on Strongly Lipschitz Domains and Some Applications","authors":"Xiaming Chen, Renjin Jiang, Dachun Yang","doi":"10.1515/agms-2016-0017","DOIUrl":"https://doi.org/10.1515/agms-2016-0017","url":null,"abstract":"Abstract Let Ω ⊂ Rn be a strongly Lipschitz domain. In this article, the authors study Hardy spaces, Hpr (Ω)and Hpz (Ω), and Hardy-Sobolev spaces, H1,pr (Ω) and H1,pz,0 (Ω) on , for p ∈ ( n/n+1, 1]. The authors establish grand maximal function characterizations of these spaces. As applications, the authors obtain some div-curl lemmas in these settings and, when is a bounded Lipschitz domain, the authors prove that the divergence equation div u = f for f ∈ Hpz (Ω) is solvable in H1,pz,0 (Ω) with suitable regularity estimates.","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2016-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/agms-2016-0017","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67166744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Isoperimetric Symmetry Breaking: a Counterexample to a Generalized Form of the Log-Convex Density Conjecture 等周对称破缺:对数凸密度猜想广义形式的一个反例
IF 1 3区 数学
Analysis and Geometry in Metric Spaces Pub Date : 2016-12-05 DOI: 10.1515/agms-2016-0014
F. Morgan
{"title":"Isoperimetric Symmetry Breaking: a Counterexample to a Generalized Form of the Log-Convex Density Conjecture","authors":"F. Morgan","doi":"10.1515/agms-2016-0014","DOIUrl":"https://doi.org/10.1515/agms-2016-0014","url":null,"abstract":"Abstract We give an example of a smooth surface of revolution for which all circles about the origin are strictly stable for fixed area but small isoperimetric regions are nearly round discs away from the origin.","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2016-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/agms-2016-0014","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67166709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 4
CMC Spheres in the Heisenberg Group 海森堡集团的CMC球体
IF 1 3区 数学
Analysis and Geometry in Metric Spaces Pub Date : 2016-11-24 DOI: 10.1515/agms-2019-0006
Valentina Franceschi, F. Montefalcone, R. Monti
{"title":"CMC Spheres in the Heisenberg Group","authors":"Valentina Franceschi, F. Montefalcone, R. Monti","doi":"10.1515/agms-2019-0006","DOIUrl":"https://doi.org/10.1515/agms-2019-0006","url":null,"abstract":"Abstract We study a family of spheres with constant mean curvature (CMC) in the Riemannian Heisenberg group H1. These spheres are conjectured to be the isoperimetric sets of H1. We prove several results supporting this conjecture. We also focus our attention on the sub-Riemannian limit.","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2016-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/agms-2019-0006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67167202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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