Differentiability properties of the isoperimetric profile in complete noncompact Riemannian manifolds with \(C^0\)-locally asymptotic bounded geometry

DOI10.1007/s40863-020-00190-4zbMath1469.49044OpenAlexW3093008047WikidataQ107168744 ScholiaQ107168744MaRDI QIDQ2042166

Abraham Enrique Muñoz Flores

Publication date: 28 July 2021

Published in: São Paulo Journal of Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40863-020-00190-4

zbMATH Keywords

finite perimeter sets\(C^0\)-locally bounded geometrydifferentiability of isoperimetric profile

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Variational problems in a geometric measure-theoretic setting (49Q20) Global Riemannian geometry, including pinching (53C20) Variational problems in infinite-dimensional spaces (58E99)

Cites Work

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• Existence of isoperimetric regions in non-compact Riemannian manifolds under Ricci or scalar curvature conditions
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• A surface with discontinuous isoperimetric profile and expander manifolds
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• On the Hamilton's isoperimetric ratio in complete Riemannian manifolds of finite volume
• Local Hölder continuity of the isoperimetric profile in complete noncompact Riemannian manifolds with bounded geometry
• Some sharp isoperimetric theorems for Riemannian manifolds
• A general comparison theorem with applications to volume estimates for submanifolds
• A complete Riemannian manifold whose isoperimetric profile is discontinuous
• Existence and characterization of regions minimizing perimeter under a volume constraint inside Euclidean cones

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