Stable constant-mean-curvature hypersurfaces are area minimizing in small \(L^1\) neighborhoods

DOI10.4171/IFB/230zbMath1195.49055arXiv0811.3126MaRDI QIDQ5962414

Antonio Ros, Frank Morgan

Publication date: 22 September 2010

Published in: Interfaces and Free Boundaries (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0811.3126

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

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Quantitative minimality of strictly stable extremal submanifolds in a flat neighbourhood, Minimality via second variation for a nonlocal isoperimetric problem, Stability in shape optimization with second variation, A selection principle for the sharp quantitative isoperimetric inequality, The Riemannian quantitative isoperimetric inequality, Volume-constrained minimizers for the prescribed curvature problem in periodic media, Morse index of multiplicity one min-max minimal hypersurfaces, Large isoperimetric regions in the product of a compact manifold with Euclidean space, A mountain-pass theorem for asymptotically conical self-expanders, Minimizers of the prescribed curvature functional in a Jordan domain with no necks

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