Isoperimetry with upper mean curvature bounds and sharp stability estimates

• DOI: 10.1007/s00526-017-1139-3
• Publication Date: 2017-03-24T09:40:26Z
• Authors: B. Krummel; F. Maggi
• Keywords: Optimization and Control (math.OC); FOS: Mathematics; 0101 mathematics; Mathematics - Optimization and Control; 01 natural sciences

42 pages. This version 2 includes a strong improvement of Theorem 1.10, plus some minor corrections<br/>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.<br/>