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Complex Analysis: The Geometric Viewpoint: Carus Mathematical Monographs, cartea 23

Autor Steven G. Krantz
en Limba Engleză Hardback – 8 sep 2004
In this second edition of a Carus Monograph Classic, Steven G. Krantz, a leading worker in complex analysis and a winner of the Chauvenet Prize for outstanding mathematical exposition, 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 disk. He also introduces the Bergmann kernel and metric and provides profound applications, some of which have never appeared in print before. In general, the new edition represents a considerable polishing and re-thinking of the original successful volume. A minimum of geometric formalism is used to gain a maximum of geometric and analytic insight. The climax of the book is an introduction to several complex variables from the geometric viewpoint. Poincaré's theorem, that the ball and bidisc are biholomorphically inequivalent, is discussed and proved.
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Specificații

ISBN-13: 9780883850350
ISBN-10: 0883850354
Pagini: 234
Ilustrații: 38 b/w illus. 10 exercises
Dimensiuni: 153 x 219 x 21 mm
Greutate: 0 kg
Ediția:Revizuită
Editura: The Mathematical Association of America
Colecția The Mathematical Association of America
Seria Carus Mathematical Monographs

Locul publicării:Washington DC, United States

Cuprins

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.

Recenzii

'A first-rate book, which can be used either as a text or a 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

Descriere

Advanced textbook on central topic of pure mathematics.