UID:
almahu_9947363166502882
Format:
XIII, 208 p.
,
online resource.
ISBN:
9783322802712
Series Statement:
Aspects of Mathematics, 21
Note:
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.
In:
Springer eBooks
Additional Edition:
Printed edition: ISBN 9783322802736
Language:
English
DOI:
10.1007/978-3-322-80271-2
URL:
http://dx.doi.org/10.1007/978-3-322-80271-2
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