  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.
