The Wulff theorem revisited

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