{"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":null,"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":"72 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2016-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/agms-2016-0014","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis and Geometry in Metric Spaces","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/agms-2016-0014","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 4
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.
期刊介绍:
Analysis and Geometry in Metric Spaces is an open access electronic journal that publishes cutting-edge research on analytical and geometrical problems in metric spaces and applications. We strive to present a forum where all aspects of these problems can be discussed.
AGMS is devoted to the publication of results on these and related topics:
Geometric inequalities in metric spaces,
Geometric measure theory and variational problems in metric spaces,
Analytic and geometric problems in metric measure spaces, probability spaces, and manifolds with density,
Analytic and geometric problems in sub-riemannian manifolds, Carnot groups, and pseudo-hermitian manifolds.
Geometric control theory,
Curvature in metric and length spaces,
Geometric group theory,
Harmonic Analysis. Potential theory,
Mass transportation problems,
Quasiconformal and quasiregular mappings. Quasiconformal geometry,
PDEs associated to analytic and geometric problems in metric spaces.