On the boundary of almost isoperimetric domains

Erwann Aubry; Jean-François Grosjean

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arXiv · 1703.02587

On the boundary of almost isoperimetric domains

Erwann Aubry·Jean-François Grosjean

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Abstract

We prove that finite perimeter subsets of $\mathbb{R}^{n+1}$ with small isoperimetric deficit have boundary Hausdorff-close to a sphere up to a subset of small measure. We also refine this closeness under some additional a priori integral curvature bounds. As an application, we answer a question raised by B. Colbois concerning the almost extremal hypersurfaces for Chavel's inequality.

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BibTeX RIS

Erwann Aubry, Jean-François Grosjean. 2017-03-07. On the boundary of almost isoperimetric domains. https://arxiv.org/abs/1703.02587

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