Alexandrov's theorem revisited
arXiv:1711.07690 · doi:10.2140/apde.2019.12.1613
Abstract
We show that among sets of finite perimeter balls are the only volume-constrained critical points of the perimeter functional.
Version 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