Submanifolds, Isoperimetric Inequalities and Optimal Transportation

Details Submanifolds, Isoperimetric Inequalities and Optimal Transportation Submanifolds, Isoperimetric Inequalities and Optimal Transportation

2009-08-19

arxiv.org/abs/0908.2711v1

Mathematics

Differential Geometry

Scientific paper

The aim of this paper is to prove isoperimetric inequalities on submanifolds of the Euclidean space using mass transportation methods. We obtain a sharp ?weighted isoperimetric inequality? and a nonsharp classical inequality similar to the one obtained by J. Michael and L. Simon. The proof relies on the description of a solution of the problem of Monge when the initial measure is supported in a submanifold and the ?nal one supported in a linear subspace of the same dimension.

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