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

2022/05/20 by S. Brendle, Brendle, S., M. Eichmair +1 · 3 citations
Mathematics · #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2205.10284

Abstract

We give an alternative proof of the Michael-Simon-Sobolev inequality using techniques from optimal transport. The inequality is sharp for submanifolds of codimension 2.

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