# Isoperimetry with upper mean curvature bounds and sharp stability estimates

created by maggi on 02 Jun 2016
modified on 25 Apr 2018

[BibTeX]

Submitted Paper

Inserted: 2 jun 2016
Last Updated: 25 apr 2018

Journal: Calc. Var. PDE
Year: 2017

Abstract:

It was proved by Almgren that among boundaries whose mean curvature is bounded from above, perimeter is uniquely minimized by balls. We obtain sharp stability estimates for Almgren's isoperimetric principle and, as an application, we deduce a sharp description of boundaries with almost constant mean curvature under a total perimeter bound which prevents bubbling.