THE LOGARITHMIC SOBOLEV INEQUALITY FOR A SUBMANIFOLD IN MANIFOLDS WITH ASYMPTOTICALLY NONNEGATIVE SECTIONAL CURVATURE*

doi:10.1007/s10473-024-0110-6

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (1): 189-194.doi: 10.1007/s10473-024-0110-6

THE LOGARITHMIC SOBOLEV INEQUALITY FOR A SUBMANIFOLD IN MANIFOLDS WITH ASYMPTOTICALLY NONNEGATIVE SECTIONAL CURVATURE^*

Yuxin Dong¹, Hezi Lin², Lingen Lu^1,†

1. School of Mathematical Sciences, Fudan University, Shanghai 20043, China;
2. School of Mathematics and Statistics & Laboratory of Analytical Mathematics and Applications ($Ministry of Education$) & FJKLMAA, Fujian Normal University, Fuzhou 350108, China

收稿日期:2022-10-01 修回日期:2023-08-03 出版日期:2024-02-25 发布日期:2024-02-27
通讯作者: † Lingen Lu, E-mail: lulingen@fudan.edu.cn
作者简介:Yuxin Dong, E-mail: yxdong@fudan.edu.cn; Hezi Lin, E-mail: lhz1@fjnu.edu.cn

THE LOGARITHMIC SOBOLEV INEQUALITY FOR A SUBMANIFOLD IN MANIFOLDS WITH ASYMPTOTICALLY NONNEGATIVE SECTIONAL CURVATURE^*

Yuxin Dong¹, Hezi Lin², Lingen Lu^1,†

1. School of Mathematical Sciences, Fudan University, Shanghai 20043, China;
2. School of Mathematics and Statistics & Laboratory of Analytical Mathematics and Applications ($Ministry of Education$) & FJKLMAA, Fujian Normal University, Fuzhou 350108, China

Received:2022-10-01 Revised:2023-08-03 Online:2024-02-25 Published:2024-02-27
Contact: † Lingen Lu, E-mail: lulingen@fudan.edu.cn
About author:Yuxin Dong, E-mail: yxdong@fudan.edu.cn; Hezi Lin, E-mail: lhz1@fjnu.edu.cn

摘要/Abstract

摘要： In this note, we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature. Like the Michale-Simon Sobolev inequality, this inequality contains a term involving the mean curvature.

关键词: asymptotically nonnegative sectional curvature, logarithmic Sobolev inequality, ABP method

Abstract: In this note, we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature. Like the Michale-Simon Sobolev inequality, this inequality contains a term involving the mean curvature.

Key words: asymptotically nonnegative sectional curvature, logarithmic Sobolev inequality, ABP method

中图分类号:

35R45

Yuxin Dong, Hezi Lin, Lingen Lu. THE LOGARITHMIC SOBOLEV INEQUALITY FOR A SUBMANIFOLD IN MANIFOLDS WITH ASYMPTOTICALLY NONNEGATIVE SECTIONAL CURVATURE^*[J]. 数学物理学报(英文版), 2024, 44(1): 189-194.

Yuxin Dong, Hezi Lin, Lingen Lu. THE LOGARITHMIC SOBOLEV INEQUALITY FOR A SUBMANIFOLD IN MANIFOLDS WITH ASYMPTOTICALLY NONNEGATIVE SECTIONAL CURVATURE^*[J]. Acta mathematica scientia,Series B, 2024, 44(1): 189-194.

THE LOGARITHMIC SOBOLEV INEQUALITY FOR A SUBMANIFOLD IN MANIFOLDS WITH ASYMPTOTICALLY NONNEGATIVE SECTIONAL CURVATURE^*

THE LOGARITHMIC SOBOLEV INEQUALITY FOR A SUBMANIFOLD IN MANIFOLDS WITH ASYMPTOTICALLY NONNEGATIVE SECTIONAL CURVATURE^*

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