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

2021/04/11 by Yi, Chengyang, Zheng, Yu
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2104.05045

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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