Acta mathematica scientia,Series B ›› 2024, Vol. 44 ›› Issue (1): 189-194.doi: 10.1007/s10473-024-0110-6

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

Yuxin Dong1, Hezi Lin2, Lingen Lu1,†   

  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

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

CLC Number: 

  • 35R45
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