The Logarithmic Sobolev Inequality for a Submanifold in Manifolds with Nonnegative Sectional Curvature

Chengyang Yi; Yu Zheng

doi:10.1007/s11401-024-0024-6

The Logarithmic Sobolev Inequality for a Submanifold in Manifolds with Nonnegative Sectional Curvature

Chengyang Yi^*
, Yu Zheng^*

^*此作品的通讯作者

数学科学学院

East China Normal University

科研成果: 期刊稿件 › 文章 › 同行评审

2 引用（Scopus）

摘要

The authors prove a sharp logarithmic Sobolev inequality which holds for compact submanifolds without boundary in Riemannian manifolds with nonnegative sectional curvature of arbitrary dimension and codimension. Like the Michael-Simon Sobolev inequality, this inequality includes a term involving the mean curvature. This extends a recent result of Brendle with Euclidean setting.

源语言	英语
页（从-至）	487-496
页数	10
期刊	Chinese Annals of Mathematics. Series B
卷	45
期	3
DOI	https://doi.org/10.1007/s11401-024-0024-6
出版状态	已出版 - 5月 2024

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10.1007/s11401-024-0024-6

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abstract = "The authors prove a sharp logarithmic Sobolev inequality which holds for compact submanifolds without boundary in Riemannian manifolds with nonnegative sectional curvature of arbitrary dimension and codimension. Like the Michael-Simon Sobolev inequality, this inequality includes a term involving the mean curvature. This extends a recent result of Brendle with Euclidean setting.",

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AU - Yi, Chengyang

AU - Zheng, Yu

N1 - Publisher Copyright: © The Editorial Office of CAM and Springer-Verlag Berlin Heidelberg 2024.

PY - 2024/5

Y1 - 2024/5

N2 - The authors prove a sharp logarithmic Sobolev inequality which holds for compact submanifolds without boundary in Riemannian manifolds with nonnegative sectional curvature of arbitrary dimension and codimension. Like the Michael-Simon Sobolev inequality, this inequality includes a term involving the mean curvature. This extends a recent result of Brendle with Euclidean setting.

AB - The authors prove a sharp logarithmic Sobolev inequality which holds for compact submanifolds without boundary in Riemannian manifolds with nonnegative sectional curvature of arbitrary dimension and codimension. Like the Michael-Simon Sobolev inequality, this inequality includes a term involving the mean curvature. This extends a recent result of Brendle with Euclidean setting.

KW - Logarithmic Sobolev inequality

KW - Nonnegative sectional curvature

KW - Submanifold

UR - https://www.scopus.com/pages/publications/85195120970

U2 - 10.1007/s11401-024-0024-6

DO - 10.1007/s11401-024-0024-6

M3 - 文章

AN - SCOPUS:85195120970

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JO - Chinese Annals of Mathematics. Series B

JF - Chinese Annals of Mathematics. Series B

IS - 3

ER -

The Logarithmic Sobolev Inequality for a Submanifold in Manifolds with Nonnegative Sectional Curvature

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