Existence and topological uniqueness of compact CMC hypersurfaces with boundary in hyperbolic space

DOI10.1007/S12220-012-9324-2zbMath1282.53052OpenAlexW2016581065MaRDI QIDQ375745

Rafael López, Luis J. Alías, Jaime Bruck Ripoll

Publication date: 31 October 2013

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12220-012-9324-2

zbMATH Keywords

hyperbolic spaceconstant mean curvature\(H\)-hypersphereAlexandrov reflection methodhyperbolic Killing graphs

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) Other special differential geometries (53A40)

Related Items (1)

Quantitative stability for hypersurfaces with almost constant mean curvature in the hyperbolic space

Cites Work

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• Constant mean curvature surfaces in a half-space of \(\mathbb{R}^ 3\) with boundary in the boundary of the half-space
• A note on \(H\)-surfaces with boundary
• Elliptic partial differential equations of second order
• A characteristic property of spherical caps
• An extension of a theorem of Serrin to graphs in warped products

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