
Complex Analysis
The Geometric Viewpoint
Steven G. Krantz(Author)
Mathematical Association of America (Publisher)
2nd Edition
Will be published approx. on 30. December 2003
Book
Hardback
234 pages
978-0-88385-035-0 (ISBN)
Description
In this second edition of a Carus Monograph Classic, Steven Krantz develops material on classical non-Euclidean geometry. He shows how it can be developed in a natural way from the invariant geometry of the complex disc. He also introduces the Bergman kernel and metric and provides profound applications, some of them never having appeared before in print. In general, the new edition represents a considerable polishing and re-thinking of the original successful volume. This is the first and only book to describe the context, the background, the details, and the applications of Ahlfors's celebrated ideas about curvature, the Schwarz lemma, and applications in complex analysis. Beginning from scratch, and requiring only a minimal background in complex variable theory, this book takes the reader up to ideas that are currently active areas of study. Such areas include a) the Caratheodory and Kobayashi metrics, b) the Bergman kernel and metric, c) boundary continuation of conformal maps. There is also an introduction to the theory of several complex variables. Poincar 's celebrated theorem about the biholomorphic inequivalence of the ball and polydisc is discussed and proved.
Reviews / Votes
A first-rate book, which can be used either as a text or reference."" - Choice""In five very nicely written chapters this book gives an introduction to the approach to function theory via Riemannian geometry. Very little function-theoretic background is needed and no knowledge whatsoever of differential geometry is assumed."" - Mathematical Reviews
More details
Series
Edition
Second Edition
Language
English
Place of publication
Washington DC
United States
Target group
Professional and scholarly
Edition type
New edition
Product notice
sewn/stitched
Cloth over boards
Dimensions
Height: 228 mm
Width: 152 mm
Thickness: 21 mm
Weight
395 gr
ISBN-13
978-0-88385-035-0 (9780883850350)
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Schweitzer Classification
Other editions
Previous edition

Kunihiko Kodaira
Complex Analysis
Book
08/2007
Cambridge University Press
€114.30
Shipment within 15-20 days
Content
Preface; Principal ideas of classical function theory; 1. Basic notions of differential geometry; 2. Curvature and applications; 3. Some new invariant metrics; 4. Introduction to the Bergmann theory; 5. A glimpse of several complex variables; 6. Appendix; Symbols; References; Index.