Generalized compactness for finite perimeter sets and applications to the isoperimetric problem

DOI10.1007/S10883-020-09517-YzbMath1481.49047arXiv1504.05104OpenAlexW3093815903MaRDI QIDQ2070347

Stefano Nardulli, Abraham Enrique Muñoz Flores

Publication date: 24 January 2022

Published in: Journal of Dynamical and Control Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.05104

zbMATH Keywords

isoperimetric profileexistence of isoperimetric region

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) Variational problems in infinite-dimensional spaces (58E99)

Related Items (3)

The isoperimetric problemviadirect method in noncompact metric measure spaces with lower Ricci bounds ⋮ Pointed Gromov-Hausdorff topological stability for non-compact metric spaces ⋮ The isoperimetric problem on Riemannian manifolds via Gromov–Hausdorff asymptotic analysis

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Existence of isoperimetric regions in non-compact Riemannian manifolds under Ricci or scalar curvature conditions
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• Clusters minimizing area plus length of singular curves
• Analysis on geodesic balls of sub-elliptic operators
• Generalized existence of isoperimetric regions in non-compact Riemannian manifolds and applications to the isoperimetric profile
• Local Hölder continuity of the isoperimetric profile in complete noncompact Riemannian manifolds with bounded geometry
• Some sharp isoperimetric theorems for Riemannian manifolds
• Riemannian Geometry
• Regularity of isoperimetric hypersurfaces in Riemannian manifolds
• Heat semigroup and functions of bounded variation on Riemannian manifolds

This page was built for publication: Generalized compactness for finite perimeter sets and applications to the isoperimetric problem