Alexandrov's theorem revisited
Analysis of PDEs
2019-03-13 v2 Differential Geometry
Abstract
We show that among sets of finite perimeter balls are the only volume-constrained critical points of the perimeter functional.
Cite
@article{arxiv.1711.07690,
title = {Alexandrov's theorem revisited},
author = {M. G. Delgadino and F. Maggi},
journal= {arXiv preprint arXiv:1711.07690},
year = {2019}
}
Comments
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