Isoperimetry with upper mean curvature bounds and sharp stability estimates
Optimization and Control
2016-08-16 v2
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.
Cite
@article{arxiv.1606.00490,
title = {Isoperimetry with upper mean curvature bounds and sharp stability estimates},
author = {Brian Krummel and Francesco Maggi},
journal= {arXiv preprint arXiv:1606.00490},
year = {2016}
}
Comments
42 pages. This version 2 includes a strong improvement of Theorem 1.10, plus some minor corrections