Stable constant mean curvature surfaces minimize area

DOI10.2140/pjm.1996.175.527zbMath0878.49026OpenAlexW2141529403MaRDI QIDQ1359207

Karsten Grosse-Brauckmann

Publication date: 14 December 1997

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2140/pjm.1996.175.527

zbMATH Keywords

area minimizationarea functionalfoliationsmean curvature surfaces

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Optimization of shapes other than minimal surfaces (49Q10) Foliations (differential geometric aspects) (53C12)

Related Items (12)

A note on \(\mu\)-stable surfaces with prescribed constant mean curvature ⋮ Embedded 𝐻-planes in hyperbolic 3-space ⋮ Minimality via second variation for a nonlocal isoperimetric problem ⋮ Stability in shape optimization with second variation ⋮ Moduli Spaces of Singular Yamabe Metrics ⋮ Gyroids of Constant Mean Curvature ⋮ Generalizations of the Choe-Hoppe helicoid and Clifford cones in Euclidean space ⋮ Embeddedness of the solutions to the \(H\)-Plateau problem ⋮ Minimizing constant mean curvature hypersurfaces in hyperbolic space ⋮ Large isoperimetric regions in the product of a compact manifold with Euclidean space ⋮ Stable constant-mean-curvature hypersurfaces are area minimizing in small \(L^1\) neighborhoods ⋮ The periodic isoperimetric problem

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