Optimal Transport Approach to Michael-Simon-Sobolev Inequalities in Manifolds with Intermediate Ricci Curvature Lower Bounds

Abstract

We generalize McCann's theorem of optimal transport to a submanifold setting and prove Michael-Simon-Sobolev inequalities for submanifolds in manifolds with lower bounds on intermediate Ricci curvatures. The results include a variant of the sharp Michael-Simon-Sobolev inequality in S. Brendle's work arXiv:2009.13717 when the intermediate Ricci curvatures are nonnegative.

arXiv comment26 pages. Minor changes and references added. Final version

References in corpus (5)

• Sharp and rigid isoperimetric inequalities in metric-measure spaces with lower Ricci curvature bounds
• On asymptotically harmonic manifolds of negative curvature
• Submanifolds, Isoperimetric Inequalities and Optimal Transportation
• Asymptotic isoperimetry on non collapsed spaces with lower Ricci bounds
• Sectional and intermediate Ricci curvature lower bounds via Optimal Transport