Value distribution of the Gauss map of improper affine spheres - Mathematics > Differential GeometryReport as inadecuate




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Abstract: We give the best possible upper bound for the number of exceptional values ofthe Lagrangian Gauss map of complete improper affine fronts in the affinethree-space. We also obtain the sharp estimate for weakly complete case. As anapplication of this result, we provide a new and simple proof of the parametricaffine Bernstein problem for improper affine spheres. Moreover we get the sameestimate for the ratio of canonical forms of weakly complete flat fronts inhyperbolic three-space.



Author: Yu Kawakami, Daisuke Nakajo

Source: https://arxiv.org/







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