Proof of the Michael-Simon-Sobolev inequality using optimal transport

DOI10.1515/crelle-2023-0054arXiv2205.10284OpenAlexW4386308120MaRDI QIDQ6060806

Michael Eichmair, Simon Brendle

Publication date: 6 November 2023

Published in: Journal für die Reine und Angewandte Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2205.10284

Mathematics Subject Classification ID

Real functions (26-XX) Functional analysis (46-XX)

Related Items (2)

A sharp Sobolev principle on the graphic submanifolds of \(\mathbb{R}^{n+m}\) ⋮ Optimal transport approach to Michael-Simon-Sobolev inequalities in manifolds with intermediate Ricci curvature lower bounds

Cites Work

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• The isoperimetric inequality for a minimal submanifold in Euclidean space
• Sobolev and mean‐value inequalities on generalized submanifolds of Rⁿ
• Optimal Transport
• Polar factorization of maps on Riemannian manifolds
• Minimal hypersurfaces and geometric inequalities

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