Constant mean curvature spheres in homogeneous three-manifolds

DOI10.1007/s00222-020-01008-yOpenAlexW3096354265MaRDI QIDQ2661175

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

Publication date: 1 April 2021

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.09394

zbMATH Keywords

Jacobi functionmetric Lie groupsCheeger constantstability operatorambient isometryCMC fluxindex-one spheresmetric semidirect productsperiodic invariant limit surfacesRiemannian universal cover

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

Constant mean curvature spheres in homogeneous three-spheres, A quasiconformal Hopf soap bubble theorem, The Gauss map of minimal surfaces in \({\mathbb{S}}^2 \times{\mathbb{R}} \), Constructions of helicoidal minimal surfaces and minimal annuli in \(\widetilde{E(2)}\), Existence of constant mean curvature 2‐Spheres in Riemannian 3‐spheres, Homogeneous hypersurfaces in symmetric spaces, Uniqueness of constant mean curvature spheres, Simons type formulas for surfaces in Sol₃ and applications, On the umbilic set of immersed surfaces in three-dimensional space forms, Dual quadratic differentials and entire minimal graphs in Heisenberg space, An extension of Ruh-Vilms’ theorem to hypersurfaces in symmetric spaces and some applications, Quantitative stability for hypersurfaces with almost constant curvature in space forms, The geometry of stable minimal surfaces in metric Lie groups, Min-max theory for constant mean curvature hypersurfaces

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