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On the maximal number of exceptional values of Gauss maps for various classes of surfaces

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Abstract

The main goal of this paper is to reveal the geometric meaning of the maximal number of exceptional values of Gauss maps for several classes of immersed surfaces in space forms, for example, complete minimal surfaces in the Euclidean three-space, weakly complete improper affine spheres in the affine three-space and weakly complete flat surfaces in the hyperbolic three-space. For this purpose, we give an effective curvature bound for a specified conformal metric on an open Riemann surface.

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Authors and Affiliations

  1. Graduate School of Science and Engineering, Yamaguchi University, Yamaguchi, 753-8512, Japan

    Yu Kawakami

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  1. Yu Kawakami
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Correspondence to Yu Kawakami.

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Partly supported by the Grant-in-Aid for Young Scientists (B) No. 24740044, Japan Society for the Promotion of Science.

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Kawakami, Y. On the maximal number of exceptional values of Gauss maps for various classes of surfaces. Math. Z. 274, 1249–1260 (2013). https://doi.org/10.1007/s00209-012-1115-8

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