## Concentration on submanifolds of positively curved homogeneous spaces

created by deponti on 15 May 2017
modified on 04 Feb 2022

[BibTeX]

Published Paper

Inserted: 15 may 2017
Last Updated: 4 feb 2022

Journal: Differential Geometry and its Applications
Year: 2017
Doi: https://doi.org/10.1016/j.difgeo.2021.101847

ArXiv: 1705.01829 PDF

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.