Vol. 12, No. 6, 2019

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Alexandrov's theorem revisited

Matias Gonzalo Delgadino and Francesco Maggi

Vol. 12 (2019), No. 6, 1613–1642
Abstract

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

Keywords
constant mean curvature, geometric measure theory, isoperimetric problem, sets of finite perimeter, varifolds, mean curvature flow
Mathematical Subject Classification 2010
Primary: 35J93, 49Q15, 49Q20, 53C21, 53C45
Milestones
Received: 29 May 2018
Revised: 1 October 2018
Accepted: 20 November 2018
Published: 7 February 2019
Authors
Matias Gonzalo Delgadino
Department of Mathematics
Imperial College London
South Kensington Campus
London
United Kingdom
Francesco Maggi
Department of Mathematics
The University of Texas at Austin
Austin, TX
United States