UID:
almahu_9947360001702882
Format:
Online-Ressource (xi, 408 p)
,
ill
Edition:
Online-Ausg. Palo Alto, Calif ebrary 2011 Electronic reproduction; Available via World Wide Web
ISBN:
3110132516 (acid-free paper)
,
9783110132519 (acid-free paper)
,
9783110870312
Series Statement:
De Gruyter expositions in mathematics 9
Content:
Invariant Distances and Metrics in Complex Analysis
Note:
Includes bibliographical references (p. [387]-399) and index
,
3.4 An extension theorem3.5 The Kobayashi-Royden pseudometric; 3.6 The Kobayashi-Buseman pseudometric; 3.7 Product-formula; Notes; Exercises; IV Contractible systems; 4.1 Abstract point of view; 4.2 Extremal problems for plurisubharmonic functions; 4.3 Inner pseudodistances. Integrated forms. Derivatives. Buseman pseudometrics. C1-pseudodistances; 4.4 Example - elementary n-circled domains; Notes; Exercises; V Contractible functions and metrics for the annulus; Notes; Exercises; VI The Bergman metric; 6.1 The Bergman kernel; 6.2 The Bergman pseudometric; 6.3 Comparison and localization.
,
6.4 The Skwarczyński pseudometricNotes; Exercises; VII Hyperbolicity and completeness; 7.1 Global hyperbolicity; 7.2 Local hyperbolicity; 7.3 Completeness - general discussion; 7.4 Carathéodory completeness; 7.5 Kobayashi completeness; 7.6 Bergman completeness; Notes; Exercises; VIII Complex geodesics. Lempert's theorem; 8.1 Complex geodesics; 8.2 Lempert's theorem; 8.3 Uniqueness of complex geodesies; 8.4 Geodesics in convex complex ellipsoids; 8.5 Biholomorphisms of complex ellipsoids; 8.6 Schwarz Lemma - the case of equality; 8.7 Criteria for biholomorphicity; Notes; Exercises.
,
E Boundary behavior of contractible metrics on weakly pseudoconvex domainsAppendix; HF Holomorphic functions; PSH Subharmonic and plurisubharmonic functions; PSC Domains of holomorphy and pseudoconvex domains; AUT Automorphisms; Automorphisms of the unit disc; Automorphisms of the unit polydisc; Automorphisms of the unit Euclidean ball; GR Green function and Dirichlet problem; MA Monge-Ampère operator; H Hardy spaces; References; List of symbols; Index.
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IX Product-propertyExercises; X Comparison on strongly pseudoconvex domains; 10.1 Strongly pseudoconvex domains; 10.2 The boundary behavior of the Carathéodory and the Kobayashi distances; 10.3 Localization; 10.4 Boundary behavior of the Carathéodory-Reiffen and the Kobayashi-Royden metrics; 10.5 A comparison of distances; 10.6 Characterization of the unit ball by its automorphism group; Notes; Exercises; Miscellanea; A The automorphism group of bounded domains; B Holomorphic curvature; C Complex geodesics; D Criteria for biholomorphicity.
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Preface; I Hyperbolic geometry of the unit disc; Exercises; II The Carathéodory pseudodistance and the Carathéodory-Reiffen pseudometric; 2.1 Definitions. General Schwarz-Pick Lemma; 2.2 Balanced domains; 2.3 Carathéodory hyperbolicity; 2.4 The Carathéodory topology; 2.5 Properties of c(*)and γ. Length of curve. Inner Carathéodory pseudodistance; 2.6 Two applications; 2.7 A class of n-circled domains; Notes; Exercises; III The Kobayashi pseudodistance and the Kobayashi-Royden pseudometric; 3.1 The Lempert function and the Kobayashi pseudodistance; 3.2 Tautness; 3.3 General properties of k.
Language:
English
DOI:
10.1515/9783110870312
URL:
http://www.degruyter.com/doi/book/10.1515/9783110870312
