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

[21] The Sharp Sobolev Inequality on Metric Measure Spaces with Lower Ricci Curvature Bounds
Profeta, Angelo
POTENTIAL ANALYSIS, 2015, 43 (03) : 513 - 529
[22] The Sharp Sobolev Inequality on Metric Measure Spaces with Lower Ricci Curvature Bounds
Angelo Profeta
Potential Analysis, 2015, 43 : 513 - 529
[23] Second-order Sobolev inequalities on a class of Riemannian manifolds with nonnegative Ricci curvature
Barbosa, Ezequiel
Kristaly, Alexandru
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2018, 50 (01) : 35 - 45
[24] Optimal transport in Lorentzian synthetic spaces, synthetic timelike Ricci curvature lower bounds and applications
Cavalletti, Fabio
Mondino, Andrea
CAMBRIDGE JOURNAL OF MATHEMATICS, 2024, 12 (02) : 417 - 534
[25] A Note on Lower Bounds Estimates for the Neumann Eigenvalues of Manifolds with Positive Ricci Curvature
Baudoin, Fabrice
Vatamanelu, Alice
POTENTIAL ANALYSIS, 2012, 37 (01) : 91 - 101
[26] The almost rigidity of manifolds with lower bounds on Ricci curvature and minimal volume growth
Sormani, C
COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 2000, 8 (01) : 159 - 212
[27] Busemann functions on manifolds with lower bounds on Ricci curvature and minimal volume growth
Sormani, C
JOURNAL OF DIFFERENTIAL GEOMETRY, 1998, 48 (03) : 557 - 585
[28] A Note on Lower Bounds Estimates for the Neumann Eigenvalues of Manifolds with Positive Ricci Curvature
Fabrice Baudoin
Alice Vatamanelu
Potential Analysis, 2012, 37 : 91 - 101
[29] Isoperimetric inequalities for finite perimeter sets under lower Ricci curvature bounds
Cavalletti, Fabio
Mondino, Andrea
RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI, 2018, 29 (03) : 413 - 430
[30] DISTANCE SPHERES AND MYERS-TYPE THEOREMS FOR MANIFOLDS WITH LOWER BOUNDS ON THE RICCI CURVATURE
ITOKAWA, Y
ILLINOIS JOURNAL OF MATHEMATICS, 1990, 34 (04) : 693 - 705

← 1 2 3 4 5 →