Lindelöf’s theorem for hyperbolic catenoids

DOI10.1090/S0002-9939-2010-10492-6zbMath1203.53054arXiv0907.4294OpenAlexW1996135805MaRDI QIDQ3053511

Ricardo Sa Earp, Pierre H. Bérard

Publication date: 29 October 2010

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0907.4294

zbMATH Keywords

domains of revolutionmaximal stable domains

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Spectral theory; eigenvalue problems on manifolds (58C40)

Related Items

Minimal hypersurfaces in \(\mathbb {H}^n \times \mathbb {R}\), total curvature and index, A new eigenvalue problem for free boundary minimal submanifolds in the unit ball, Index of the critical catenoid, Lindelöf’s theorem for hyperbolic catenoids, Stability of the classical catenoid and Darboux-Pöschl-Teller potentials, Counting minimal surfaces in quasi-Fuchsian three-manifolds, Conformal type of ends of revolution in space forms of constant sectional curvature

Cites Work

• Unnamed Item
• Unnamed Item
• Minimal hypersurfaces in \(\mathbb {H}^n \times \mathbb {R}\), total curvature and index
• Rigidity of minimal submanifolds in hyperbolic space
• A note on surfaces with prescribed oriented Euclidean Gauss map
• Lindelöf’s theorem for hyperbolic catenoids
• Stability properties for the higher dimensional catenoid in $\mathbb R^{n+1}$
• Rotation Hypersurfaces in Spaces of Constant Curvature
• The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature
• Foliation of 3-dimensional space forms by surfaces with constant mean curvature
• On the index of constant mean curvature 1 surfaces in hyperbolic space