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arXiv · 1311.1931

Function-theoretic properties for the Gauss maps of various classes of surfaces

Yu Kawakami
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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.

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Yu Kawakami. 2014-05-28. Function-theoretic properties for the Gauss maps of various classes of surfaces. https://arxiv.org/abs/1311.1931

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