English

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

R2 v1 2026-06-23T10:58:16.091Z