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arXiv · 0908.2711

Submanifolds, Isoperimetric Inequalities and Optimal Transportation

Philippe Castillon
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Abstract

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 final one supported in a linear subspace of the same dimension.

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Philippe Castillon. 2009-08-19. Submanifolds, Isoperimetric Inequalities and Optimal Transportation. https://doi.org/10.1016/j.jfa.2010.03.001

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