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Optimal Transport Approach to Michael-Simon-Sobolev Inequalities in Manifolds with Intermediate Ricci Curvature Lower Bounds (2209.06796v2)
Published 14 Sep 2022 in math.DG and math.AP
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.
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