Value Distribution Theory of the Gauss Map of Minimal Surfaces in Rm

Hirotaka Fujimoto ist Professor am Institut für Mathematik der Kanazawa Universität in Japan.

1 The Gauss map of minimal surfaces in R3.-
1.1 Minimal surfaces in Rm.-
1.2 The Gauss map of minimal surfaces in Bm.-
1.3 Enneper-Weierstrass representations of minimal surfaces in R3.-
1.4 Sum to product estimates for meromorphic functions.-
1.5 The big Picard theorem.-
1.6 An estimate for the Gaussian curvature of minimal surfaces.- 2 The derived curves of a holomorphic curve.-
2.1 Holomorphic curves and their derived curves.-
2.2 Frenet frames.-
2.3 Contact functions.-
2.4 Nochka weights for hyperplanes in subgeneral position.-
2.5 Sum to product estimates for holomorphic curves.-
2.6 Contracted curves.- 3 The classical defect relations for holomorphic curves.-
3.1 The first main theorem for holomorphic curves.-
3.2 The second main theorem for holomorphic curves.-
3.3 Defect relations for holomorphic curves.-
3.4 Borel's theorem and its applications.-
3.5 Some properties of Wronskians.-
3.6 The second main theorem for derived curves.- 4 Modified defect relation for holomorphic curves.-
4.1 Some properties of currents on a Riemann surface.-
4.2 Metrics with negative curvature.-
4.3 Modified defect relation for holomorphic curves.-
4.4 The proof of the modified defect relation.- 5 The Gauss map of complete minimal surfaces in Rm.-
5.1 Complete minimal surfaces of finite total curvature.-
5.2 The Gauss maps of minimal surfaces of finite curvature.-
5.3 Modified defect relations for the Gauss map of minimal surfaces.-
5.4 The Gauss map of complete minimal surfaces in R3 and R4.-
5.5 Examples.