Isoperimetric domains of large volume in homogeneous three-manifolds

DOI10.1016/j.aim.2014.07.025zbMath1296.53027arXiv1303.4222OpenAlexW2072481683WikidataQ56885363 ScholiaQ56885363MaRDI QIDQ400994

Joaquín Pérez, Pablo Mira, Antonio Ros, William Hamilton III Meeks

Publication date: 26 August 2014

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.4222

zbMATH Keywords

foliationCheeger constantconstant mean curvaturecritical mean curvaturehomogeneous three-manifoldisoperimetric domainmetric Lie group

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items

THE MEAN CURVATURE EQUATION ON SEMIDIRECT PRODUCTS : HEIGHT ESTIMATES AND SCHERK-LIKE GRAPHS ⋮ A Hopf theorem for non-constant mean curvature and a conjecture of A. D. Alexandrov ⋮ Constant mean curvature spheres in homogeneous three-manifolds ⋮ Rigidity of Hawking mass for surfaces in three manifolds ⋮ Uniqueness of constant mean curvature spheres ⋮ Cylinders as left invariant CMC surfaces in \(\operatorname{Sol}_3\) and \(E(\kappa,\tau)\)-spaces diffeomorphic to \(\mathbb{R}^3\)

Cites Work

• Existence of regular neighborhoods for \(H\)-surfaces
• The dynamics theorem for CMC surfaces in \(\mathbb{R}^3\)
• General curvature estimates for stable H-surfaces in 3-manifolds applications
• The isoperimetric problem in spherical cylinders
• Constant mean curvature spheres in homogeneous three-spheres
• Sur le volume minimal de ${R}\sp 2$
• Lie Groups That are Closed at Infinity
• The Cheeger constant of simply connected, solvable Lie groups
• Constant mean curvature surfaces in metric Lie groups
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