Optimal transport approach to Michael-Simon-Sobolev inequalities in manifolds with intermediate Ricci curvature lower bounds

被引：1

作者：

Wang, Kai-Hsiang ^{[1
]}

机构：

[1] Northwestern Univ, Dept Math, 2033 Sheridan Rd, Evanston, IL 60208 USA

来源：

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY | 2024年 / 65卷 / 01期

关键词：

Optimal transport; McCann's theorem; Michael-Simon inequality; Intermediate Ricci curvature; ISOPERIMETRIC-INEQUALITIES; POLAR FACTORIZATION; SHARP; REGULARITY; GEOMETRY; SPACES;

D O I：

10.1007/s10455-023-09934-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 Brendle's (arXiv:2009.13717) when the intermediate Ricci curvatures are nonnegative.

引用

页数：25

共 48 条

[41] Lower bounds for the first eigenvalue of the p-Laplace operator on compact manifolds with nonnegative Ricci curvature
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[42] Some functional inequalities under lower Bakry-Émery-Ricci curvature bounds with ε-range
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[46] Calculus of variations — isoperimetric inequalities for finite perimeter sets under lower ricci curvature bounds, by Fabio Cavalletti and Andrea Mondino, communicated on February 9, 2018
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[47] Some functional inequalities under lower Bakry–Émery–Ricci curvature bounds with ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varepsilon }$$\end{document}-range
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[48] Sharp Sobolev inequalities on noncompact Riemannian manifolds with Ric≥0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textsf{Ric}\ge 0$$\end{document} via optimal transport theory
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Calculus of Variations and Partial Differential Equations, 2024, 63 (8)

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