Value Distribution Theory of the Gauss Map of Minimal Surfaces in Rm [Paperback]

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 Borels 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.Hirotaka Fujimoto ist Professor am Institut f?r Mathematik der Kanazawa Universit?t in Japan.