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| The Logarithmic Sobolev Inequality for a Submanifold in Manifolds with Nonnegative Sectional Curvature |
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Citation： |
Chengyang YI ·,Yu ZHENG.The Logarithmic Sobolev Inequality for a Submanifold in Manifolds with Nonnegative Sectional Curvature[J].Chinese Annals of Mathematics B,2024,45(3):487~496 |
| Page view： 1045
Net amount： 643 |
Authors： |
Chengyang YI ·; Yu ZHENG |
Foundation： |
the National Natural Science Foundation of China (No. 12271163), the
Science and Technology Commission of Shanghai Municipality (No. 22DZ2229014) and Shanghai Key
Laboratory of PMMP. |
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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. |
Keywords： |
Logarithmic Sobolev inequality, Nonnegative sectional curvature,
Submanifold |
Classification： |
53C20, 53C21 |
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