Value distribution of the Gauss map of improper affine spheres

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概要

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• We give the best possible upper bounds for the number of exceptional values and totally ramified value number of the Lagrangian Gauss map of complete improper affine maps in the affine three-space. Moreover, by applying the Fujimoto argument, we also obtain the sharp estimate for them of weakly complete improper affine maps. As an application, from the viewpoint of the value distribution of Lagrangian Gauss map, we provide a new proof of the classification of affine complete improper affine spheres. Furthermore, we get a ramification estimate for the ratio of canonical forms of weakly complete flat fronts in hyperbolic three-space.

著者

• KAWAKAMI Yu

  Graduate School of Science and Engineering, Yamaguchi University

• NAKAJO Daisuke

  Faculty of Mathematics, Kyushu University

関連論文

• Value distribution of the Gauss map of improper affine spheres

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