An analogue of the UP-iteration for constant mean curvature one surfaces in hyperbolic 3-space.

DOI10.1016/J.DIFGEO.2003.10.007zbMath1088.53003OpenAlexW2051502485WikidataQ115358105 ScholiaQ115358105MaRDI QIDQ1426672

Catherine McCune, Masaaki Umehara

Publication date: 15 March 2004

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: http://cds.cern.ch/record/456543

zbMATH Keywords

Minimal surfacesSchwarzian derivativesBryant representationConstant mean curvature surfacesH-deformable surfaces

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) Non-Euclidean differential geometry (53A35) Residues for several complex variables (32A27)

Related Items (1)

Mean curvature one surfaces in hyperbolic space, and their relationship to minimal surfaces in Euclidean space

Cites Work

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• A duality on CMC-1 surfaces in hyperbolic space, and a hyperbolic analogue of the Osserman inequality
• Complete surfaces of constant mean curvature-1 in the hyperbolic 3-space
• Surfaces of constant mean curvature \(c\) in \(H^ 3(-c^ 2)\) with prescribed hyperbolic Gauss map
• A parametrization of the Weierstrass formulae and perturbation of complete minimal surfaces in R3 into the hyperbolic 3-space.
• Surfaces of Constant Mean Curvature 1 in  3 and Algebraic Curves on a Quadric
• Rational Minimal Surfaces

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