Value distribution of the Gauss map of improper affine spheres | Zendy

Yu Kawakami | Zendy; Daisuke Nakajo | Zendy

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Value distribution of the Gauss map of improper affine spheres

Author(s) -

Yu Kawakami,

Daisuke Nakajo

Publication year - 2012

Publication title -

journal of the mathematical society of japan

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.047

H-Index - 36

eISSN - 1881-1167

pISSN - 0025-5645

DOI - 10.2969/jmsj/06430799

Subject(s) - mathematics , affine transformation , affine hull , affine combination , affine coordinate system , affine space , affine shape adaptation , space (punctuation) , spheres , simple (philosophy) , gauss , complex space , mathematical analysis , affine geometry of curves , pure mathematics , parametric statistics , statistics , physics , philosophy , epistemology , quantum mechanics , astronomy , linguistics

We give the best possible upper bound for the number of exceptional values of the Lagrangian Gauss map of complete improper affine fronts in the affine three-space. We also obtain the sharp estimate for weakly complete case. As an application of this result, we provide a new and simple proof of the parametric affine Bernstein problem for improper affine spheres. Moreover, we get the same estimate for t ratio of canonical forms of weakly complete flat fronts in hyperbolic three-space.

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