
Value Distribution Theory of the Gauss Map of Minimal Surfaces in Rm
Hirotaka Fujimoto(Author)
Vieweg+Teubner Verlag
Published on 20. November 2013
Book
Paperback/Softback
XIII, 208 pages
978-3-322-80273-6 (ISBN)
Description
Hirotaka Fujimoto ist Professor am Institut für Mathematik der Kanazawa Universität in Japan.
More details
Series
Edition
Softcover reprint of the original 1st ed. 1993
Language
English
Place of publication
Wiesbaden
Germany
Publishing group
Vieweg & Teubner
Target group
Upper undergraduate
Illustrations
XIII, 208 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 13 mm
Weight
347 gr
ISBN-13
978-3-322-80273-6 (9783322802736)
DOI
10.1007/978-3-322-80271-2
Schweitzer Classification
Other editions
Additional editions

Hirotaka Fujimoto
Value Distribution Theory of the Gauss Map of Minimal Surfaces in Rm
Book
01/1993
Vieweg+Teubner Verlag
€54.99
Article exhausted; check different version
Person
Hirotaka Fujimoto ist Professor am Institut fuer Mathematik der Kanazawa Universitaet in Japan.
Content
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.