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arXiv · 2605.29567

Application of the Bloch--Ros principle to ramification theorem

Shunsuke Kasao
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Abstract

The author and Kawakami revealed that the Picard little theorem, the Carath\'{e}odory--Montel theorem and the Fujimoto theorem -- phenomena concerning omitted values in value distribution theory, normal family theory and the theory of Gauss maps of minimal surfaces, respectively -- are not isolated results but can be discussed within a unified framework. We call this theoretical framework the Bloch--Ros principle. Furthermore, the value-distribution-theoretic properties of Gauss maps hold not only for minimal surfaces but also for other classes of surfaces that admit singularities, such as maxfaces in the Lorentz--Minkowski $3$-space and improper affine fronts in the affine $3$-space, thereby further extending this theoretical framework. In this paper, we provide a unified approach to phenomena concerning totally ramified values among value distribution theory, normal family theory and the theory of Gauss maps of these classes of surfaces.

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Shunsuke Kasao. 2026-05-28. Application of the Bloch--Ros principle to ramification theorem. https://arxiv.org/abs/2605.29567

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