Existence and uniqueness of complete constant mean curvature surfaces at infinity of \({\mathbb{H}}^3\)

DOI10.1007/BF02921984zbMath0980.53076MaRDI QIDQ1589350

John A. Velling

Publication date: 11 December 2000

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

zbMATH Keywords

hyperbolic spaceconstant mean curvatureholomorphic quadratic differentialquasiconformal deformationSchwarzian differential equationsurface at infinity

Mathematics Subject Classification ID

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

Related Items (3)

LIMITATIONS ON PRESCRIBING THE HOPF DIFFERENTIAL FOR MINIMAL SURFACES IN H³ ⋮ Foliations of Hyperbolic Space by Constant Mean Curvature Surfaces Sharing Ideal Boundary ⋮ On the constructibility of a negatively curved complete surface of constant mean curvature in \(\mathbb{H}^3\) determined by a prescribed Hopf differential

Cites Work

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• Complete minimal hypersurfaces in hyperbolic n-manifolds
• Spacelike constant mean curvature surfaces in pseudo-Riemannian space forms
• The normal singularities of a submanifold
• Familles de surfaces isoparametriques dans les espaces à courbure constante
• Orthogonally integrable line fields in 3
• The hyperbolic Gauss map and quasiconformal reflections.
• A Report on Harmonic Maps
• The Schwarzian derivative and schlicht functions

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