Calculus of Variations and Geometric Measure Theory
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N. De Ponti

Concentration on submanifolds of positively curved homogeneous spaces

created by deponti on 15 May 2017
modified on 07 Jan 2020

[BibTeX]

preprint

Inserted: 15 may 2017
Last Updated: 7 jan 2020

Year: 2017

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.

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