Article contents
Function-theoretic Properties for the Gauss Maps of Various Classes of Surfaces
Published online by Cambridge University Press: 20 November 2018
Abstract
We elucidate the geometric background of function-theoretic properties for the Gauss maps of several classes of immersed surfaces in three-dimensional space forms, for example, minimal surfaces in Euclidean three-space, improper affine spheres in the affine three-space, and constant mean curvature one surfaces and flat surfaces in hyperbolic three-space. To achieve this purpose, we prove an optimal curvature bound for a specified conformal metric on an open Riemann surface and give some applications. We also provide unicity theorems for the Gauss maps of these classes of surfaces.
Keywords
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 2015
References
- 5
- Cited by