@ARTICLE{Cl04, author = {Clarenz, U.}, title = {The {Wulff-shape} minimizes an anisotropic {Willmore} functional}, journal = {Interfaces and Free Boundaries}, year = {2004}, volume = {6}, pages = {351--359}, number = {3}, abstract = {The aim of this paper is to find a fourth order energy having Wulff-shapes as minimizers. This question is motivated by surface restoration problems. In surface restoration a damaged region of a surface is replaced by a surface patch which restores the region in a suitable way. In particular one aims for $C^1$-continuity at the patch boundary. A fourth order energy is considered to measure fairness and to allow appropriate boundary conditions ensuring continuity of the normal field. Here, anisotropy comes into play if a surface is destroyed which contains edges and corners. In the present paper we define a generalization of the classical Willmore functional and prove that Wulff-shapes are the only minimizers.}, pdf = {http://numod.ins.uni-bonn.de/research/papers/public/Cl04.pdf} }