English

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

R2 v1 2026-06-22T14:15:28.067Z