Geodesic
The Wulff shape minimizes an anisotropic Willmore functional
Ulrich Clarenz1
1Bonn, Germany
Interfaces and free boundaries, Tome 6 (2004) no. 3, pp. 351-359

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DOI

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 usually a damaged region of a surface has to be 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 edges and corners of a surface are destroyed. In the present paper we define a generalization of the classical Willmore functional and prove that Wulff-shapes are the only minimizers.
DOI : 10.4171/ifb/104
Classification : 35-XX, 65-XX, 76-XX, 92-XX
Mots-clés : Wulff shapes, surface restoration, Willmore functional

Ulrich Clarenz  1

1 Bonn, Germany 
Ulrich Clarenz. The Wulff shape minimizes an anisotropic Willmore functional. Interfaces and free boundaries, Tome 6 (2004) no. 3, pp. 351-359. doi: 10.4171/ifb/104
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     year = {2004},
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     number = {3},
     doi = {10.4171/ifb/104},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/104/}
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