The Gauss map of pseudo-algebraic minimal surfaces

DOI10.1515/FORUM.2008.047zbMath1167.53010arXivmath/0511543MaRDI QIDQ3546145

Yu Kawakami, Ryoichi Kobayashi, Reiko Naka-Miyaoka

Publication date: 18 December 2008

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0511543

zbMATH Keywords

infinite total curvatureomitted valuespseudo-algebraic minimal 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)

Related Items (15)

RAMIFICATION OVER HYPERSURFACES LOCATED IN SUBGENERAL POSITION OF THE GAUSS MAP OF COMPLETE MINIMAL SURFACES WITH FINITE TOTAL CURVATURE ⋮ On the totally ramified value number of the Gauss map of minimal surfaces ⋮ On the maximal number of exceptional values of Gauss maps for various classes of surfaces ⋮ Remarks on the Gauss images of complete minimal surfaces in Euclidean four-space ⋮ Modified defect relations of the Gauss map and the total curvature of a complete minimal surface ⋮ Ramification of the Gauss map and the total curvature of a complete minimal surface ⋮ Value distribution of the Gauss map of improper affine spheres ⋮ GAUSSIAN CURVATURE AND UNICITY PROBLEM OF GAUSS MAPS OF VARIOUS CLASSES OF SURFACES ⋮ Value distribution for the Gauss maps of various classes of surfaces ⋮ Algebraic curves and the Gauss map of algebraic minimal surfaces ⋮ Unnamed Item ⋮ The classical theory of minimal surfaces ⋮ Distribution value of algebraic curves and the Gauss maps on algebraic minimal surfaces ⋮ Unicity theorem for generalized Gauss maps of immersed harmonic surfaces ⋮ Non-integrated defect relations for the Gauss maps of complete minimal surfaces with finite total curvature

Cites Work

• Unnamed Item
• On subharmonic functions and differential geometry in the large
• The topology of complete minimal surfaces of finite total Gaussian curvature
• On the number of exceptional values of the Gauss map of minimal surfaces
• Some function theoretic properties of the Gauss map for hyperbolic complete minimal surfaces
• Unicity theorems for the Gauss maps of complete minimal surfaces
• On complete minimal surfaces whose Gauss map misses two directions
• Global properties of minimal surfaces in \(E^ 3\) and \(E^ n\)
• Über ABELsche Minimalflächen
• Hyperbolic complete minimal surfaces with arbitrary topology

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