Isoperimetry with upper mean curvature bounds and sharp stability estimates

2016/06/01 by Krummel, Brian, Maggi, Francesco · 2 citations
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1606.00490

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.

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• A Dynamical Approach to the Berezin--Li--Yau Inequality
• Optimal quantitative stability estimates for Alexandrov's Soap Bubble Theorem via Gagliardo-Nirenberg-type interpolation inequalities

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