The value distribution of the hyperbolic Gauss map

DOI10.1090/S0002-9939-97-03937-3zbMath0903.53004OpenAlexW1586231880MaRDI QIDQ4356708

Zuhuan Yu

Publication date: 1 October 1997

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

Full work available at URL: https://doi.org/10.1090/s0002-9939-97-03937-3

zbMATH Keywords

Gauss maphyperbolic spaceconstant mean curvature surfaces

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Value distribution of meromorphic functions of one complex variable, Nevanlinna theory (30D35) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items

Mean curvature 1 surfaces in hyperbolic 3-space with low total curvature. II ⋮ GAUSSIAN CURVATURE AND UNICITY PROBLEM OF GAUSS MAPS OF VARIOUS CLASSES OF SURFACES ⋮ The Cauchy problem for the Liouville equation and Bryant surfaces ⋮ An analogue of minimal surface theory in 𝑆𝐿(𝑛,𝐂)/𝐒𝐔(𝐧) ⋮ Surfaces of constant mean curvature one in the hyperbolic three-space with irregular ends ⋮ Bryant surfaces in \(\mathbb H^3\) of finite type. ⋮ Mean curvature one surfaces in hyperbolic space, and their relationship to minimal surfaces in Euclidean space

Cites Work

• Unnamed Item
• Minimal surfaces in the large
• Modified defect relations for the Gauss map of minimal surfaces
• Erratum to the paper: The Gauss map of a complete non-flat minimal surface cannot omit 7 points of the sphere
• 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
• A parametrization of the Weierstrass formulae and perturbation of complete minimal surfaces in R3 into the hyperbolic 3-space.