[1] U. Clarenz. The Wulff-shape minimizes an anisotropic Willmore functional. Interfaces and Free Boundaries, 6(3):351-359, 2004.
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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 C1-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.