The logarithmic Sobolev inequality for a submanifold in manifold with nonnegative sectional curvature

Chengyang Yi; Yu Zheng

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arXiv · 2104.05045

The logarithmic Sobolev inequality for a submanifold in manifold with nonnegative sectional curvature

Chengyang Yi·Yu Zheng

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Abstract

We prove a sharp logarithmic Sobolev inequality which holds for compact submanifolds without boundary in Riemannian manifold with nonnegative sectional curvature of arbitrary dimension and codimension, while the ambient manifold needs to have a specific Euclid-like property. Like the Michael-Simon Sobolev inequality, this inequality includes a term involving the mean curvature. This extends a recent result of S. Brendle with Euclidean setting.

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BibTeX RIS

Chengyang Yi, Yu Zheng. 2021-04-11. The logarithmic Sobolev inequality for a submanifold in manifold with nonnegative sectional curvature. https://arxiv.org/abs/2104.05045

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