Research Article
Optimal Transport Approach to Michael-Simon-Sobolev Inequalities in Manifolds with Intermediate Ricci Curvature Lower Bounds
https://doi.org/10.21203/rs.3.rs-3146914/v1
This work is licensed under a CC BY 4.0 License
published 13 Dec, 2023
Read the published version in Annals of Global Analysis and Geometry →
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We generalize McCann's theorem of optimal transport to a submanifold setting and use it to 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 [arXiv:2009.13717] when the intermediate Ricci curvatures are nonnegative.
2020 Mathematics Subject Classification. Primary 53C21, 49Q22; Secondary 53C23.
optimal transport
McCann’s theorem
Michael-Simon inequality
intermediate Ricci curvature.
No competing interests reported.
published 13 Dec, 2023
Read the published version in Annals of Global Analysis and Geometry →
Editorial decision: Accepted
03 Nov, 2023
Reviews received at journal
01 Nov, 2023
Reviewers agreed at journal
28 Jul, 2023
Reviewers invited by journal
20 Jul, 2023
Editor assigned by journal
12 Jul, 2023
Submission checks completed at journal
07 Jul, 2023
First submitted to journal
06 Jul, 2023
You are reading this latest preprint version