The logarithmic Sobolev inequality for a submanifold in Euclidean space

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.

final version, to appear in Comm Pure Appl Math

References in corpus (2)

• On asymptotically harmonic manifolds of negative curvature
• Submanifolds, Isoperimetric Inequalities and Optimal Transportation