Calculus of Variations and Geometric Measure Theory

N. De Ponti

Concentration on submanifolds of positively curved homogeneous spaces

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


Published Paper

Inserted: 15 may 2017
Last Updated: 4 feb 2022

Journal: Differential Geometry and its Applications
Year: 2017

ArXiv: 1705.01829 PDF


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.