The logarithmic Sobolev inequality for a submanifold in Euclidean space
Differential Geometry
2020-10-07 v3 Analysis of PDEs
Abstract
We prove a sharp logarithmic Sobolev inequality which holds for submanifolds in Euclidean space of arbitrary dimension and codimension. Like the Michael-Simon Sobolev inequality, this inequality includes a term involving the mean curvature.
Keywords
Cite
@article{arxiv.1908.10360,
title = {The logarithmic Sobolev inequality for a submanifold in Euclidean space},
author = {S. Brendle},
journal= {arXiv preprint arXiv:1908.10360},
year = {2020}
}
Comments
final version, to appear in Comm Pure Appl Math