Continuity of the isoperimetric profile of a complete Riemannian manifold under sectional curvature conditions

DOI10.4171/RMI/935zbMath1375.49058arXiv1503.07014WikidataQ115211813 ScholiaQ115211813MaRDI QIDQ520721

Manuel Ritoré

Publication date: 5 April 2017

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.07014

zbMATH Keywords

convex setspositive curvatureisoperimetric profileHadamard manifoldsstrictly convex functions

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Optimization of shapes other than minimal surfaces (49Q10)

Related Items (12)

Sobolev embeddings into Orlicz spaces and isocapacitary inequalities ⋮ Isoperimetric inequalities in unbounded convex bodies ⋮ Existence of self-Cheeger sets on Riemannian manifolds ⋮ A surface with discontinuous isoperimetric profile and expander manifolds ⋮ Isoperimetric rigidity and distributions of 1-Lipschitz functions ⋮ Bounds for eigenfunctions of the Neumann \(p\)-Laplacian on noncompact Riemannian manifolds ⋮ A reciprocity principle for constrained isoperimetric problems and existence of isoperimetric subregions in convex sets ⋮ Differentiability properties of the isoperimetric profile in complete noncompact Riemannian manifolds with \(C^0\)-locally asymptotic bounded geometry ⋮ Local Hölder continuity of the isoperimetric profile in complete noncompact Riemannian manifolds with bounded geometry ⋮ Total curvature and the isoperimetric inequality in Cartan-Hadamard manifolds ⋮ Uniform Lipschitz continuity of the isoperimetric profile of compact surfaces under normalized Ricci flow ⋮ On the existence of isoperimetric regions in manifolds with nonnegative Ricci curvature and Euclidean volume growth

Cites Work

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• Manifolds of nonpositive curvature
• \(C^\infty\) convex functions and manifolds of positive curvature
• Existence of isoperimetric regions in contact sub-Riemannian manifolds
• On the structure of complete manifolds of nonnegative curvature
• A new isoperimetric comparison theorem for surfaces of variable curvature
• Sur le volume minimal de ${R}\sp 2$
• Some isoperimetric comparison theorems for convex bodies in Riemannian

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