A study on the relationship between the global property of immersed surfaces in space forms and the behavior of their Gauss maps

2014 Fiscal Year Final Research Report

• Project/Area Number: 24740044
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Kanazawa University (2014); Yamaguchi University (2012-2013)
• Principal Investigator: KAWAKAMI Yu 金沢大学, 数物科学系, 准教授 (60532356)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 幾何学 / 函数論 / 曲面論 / 値分布論 / ガウス写像 / 波面（フロント） / 除外値 / 一意性定理

Outline of Final Research Achievements

We elucidated the geometric background of function-theoretic properties for the Gauss maps of several classes of immersed surfaces in three-dimensional space forms, for example, minimal surfaces in Euclidean three-space, improper affine spheres in the affine three-space and flat surfaces in hyperbolic three-space. In particular, we give an effective curvature bound for a specified conformal metric on an open Riemann surface. As an application of the result, we revealed the geometric meaning of the maximal number of exceptional values of Gauss maps for these surfaces.

Free Research Field

幾何学