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Article Dans Une Revue Journal of Functional Analysis Année : 2010

Submanifolds, Isoperimetric Inequalities and Optimal Transportation

Résumé

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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Dates et versions

hal-00410264 , version 1 (19-08-2009)

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Philippe Castillon. Submanifolds, Isoperimetric Inequalities and Optimal Transportation. Journal of Functional Analysis, 2010, 259, pp.79-103. ⟨10.1016/j.jfa.2010.03.001⟩. ⟨hal-00410264⟩
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