Calculus of Variations and Geometric Measure Theory
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N. De Ponti

A concentration result on submanifolds of compact positively curved homogeneous spaces

created by deponti on 15 May 2017



Inserted: 15 may 2017

Year: 2017

ArXiv: 1705.01829 PDF


Concentration of measure is a principle that informally states that in some spaces any Lipschitz function is essentially constant on a set of almost full measure. From a geometric point of view, it is very important to find some structured subsets on which this phenomenon occurs. In this paper, I generalize a well-known result on the sphere due to Milman to a class of Riemannian manifolds. I prove that any Lipschitz function on a compact, positively curved, homogeneous space is almost constant on a high dimensional submanifold.

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