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A uniqueness proof for the Wulff Theorem

Published online by Cambridge University Press:  14 November 2011

Irene Fonseca  and
Stefan Müller
Irene Fonseca
Affiliation:
Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213, U.S.A.
Stefan Müller
Affiliation:
Institut für Angewandte Mathematik, Universität Bonn, Beringstr. 4, W-5300 Bonn 1, Germany
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Synopsis

The Wulff problem is a generalisation of the isoperimetric problem and is relevant for the equilibrium of (small) elastic crystals. It consists in minimising the (generally anisotropic) surface energy among sets of given volume. A solution of this problem is given by a geometric construction due to Wulff. In the class of sets of finite perimeter this was first shown by J. E. Taylor who, using methods of geometric measure theory, also proved uniqueness. Here a more analytic uniqueness proof is presented. The main ingredient is a sharpened version of the Brunn–Minkowski inequality.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 119 , Issue 1-2 , 1991 , pp. 125 - 136
Copyright
Copyright © Royal Society of Edinburgh 1991

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