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

Chengyang Yi , Yu Zheng

Chinese Annals of Mathematics, Series B ›› 2024, Vol. 45 ›› Issue (3) : 487 -496.

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Chinese Annals of Mathematics, Series B ›› 2024, Vol. 45 ›› Issue (3) : 487 -496. DOI: 10.1007/s11401-024-0024-6
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The Logarithmic Sobolev Inequality for a Submanifold in Manifolds with Nonnegative Sectional Curvature

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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

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Chengyang Yi, Yu Zheng. The Logarithmic Sobolev Inequality for a Submanifold in Manifolds with Nonnegative Sectional Curvature. Chinese Annals of Mathematics, Series B, 2024, 45(3): 487-496 DOI:10.1007/s11401-024-0024-6

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