Analysis & PDE 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

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.

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