Concentration on submanifolds of positively curved homogeneous spaces

Abstract

A classical result of Milman roughly states that every Lipschitz function on ${\mathbb{S}}^n$ is almost constant on a sufficiently high-dimensional sphere ${\mathbb{S}}^m\subset {\mathbb{S}}^n$. In this paper we extend the result by proving that any Lipschitz function on a positively curved homogeneous space is almost constant on a high dimensional submanifold.

arXiv commentImproved overall quality of presentation; fixed some minor errors