Alexandrov's theorem revisited

Abstract

We show that among sets of finite perimeter balls are the only volume-constrained critical points of the perimeter functional.

arXiv commentVersion 2: Remarks on Wente's tori and volume-preserving mean curvature flows added. More detailed description of the main proof added. Theorem 2 in version 1 (Wulff shapes are the only local minimizers of anisotropic energies) has been moved to a separate preprint

References in corpus (2)

• Alexandrov's theorem revisited
• Bubbling with $L^2$-almost constant mean curvature and an Alexandrov-type theorem for crystals

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