Isoperimetric symmetry breaking: a counterexample to a generalized form of the log-convex density conjecture

DOI10.1515/AGMS-2016-0014zbMath1355.53005OpenAlexW2560656289WikidataQ122899141 ScholiaQ122899141MaRDI QIDQ729692

Frank Morgan

Publication date: 22 December 2016

Published in: Analysis and Geometry in Metric Spaces (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/agms-2016-0014

zbMATH Keywords

symmetry breakingisoperimetric

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Optimization of shapes other than minimal surfaces (49Q10) Surfaces in Euclidean and related spaces (53A05)

Related Items (2)

Some isoperimetric inequalities in the plane with radial power weights ⋮ Some weighted isoperimetric problems on \({\mathbb{R}}^N_+\) with stable half balls have no solutions

Cites Work

• Double bubbles on the real line with log-convex density
• The log-convex density conjecture and vertical surface area in warped products
• Isoperimetric problems on the sphere and on surfaces with density
• Constant geodesic curvature curves and isoperimetric domains in rotationally symmetric surfaces
• Proof of the log-convex density conjecture
• Some sharp isoperimetric theorems for Riemannian manifolds
• The isoperimetric problem on surfaces of revolution of decreasing Gauss curvature
• A volume preserving flow and the isoperimetric problem in warped product spaces

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