The Wulff Theorem Revisited

Irene Fonseca

Abstract

The parametrized indicator measures and the Brunn-Minkowski inequality are used to prove that the Wulff set W$_{\Gamma}$ is a minimizer for the surface energy where the density is the support function of W$_{\Gamma}$. The support of the indicator measures associated to minimizing sequences is characterized. It is shown that if W$_{\Gamma}$ is polyhedral then minimizing sequences cannot oscillate.

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