Complex analysis : the geometric viewpoint /
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 kernal and metric and provides profound applicat...
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| Online Access: |
Full text (MCPHS users only) |
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| Main Author: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
[Washington?] :
Mathematical Association of America,
2004
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| Edition: | 2nd ed. |
| Series: | Carus mathematical monographs ;
no. 23. |
| Subjects: | |
| Local Note: | ProQuest Ebook Central |
| Summary: | 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 kernal 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. Poincaré's celebrated theorem about the biholomorphic inequivalence of the ball and polydisc is discussed and proved. |
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| Physical Description: | 1 online resource (xvii, 219 pages) : illustrations |
| Bibliography: | Includes bibliographical references (pages 209-211) and index. |
| ISBN: | 0883850354 9780883850350 0883850001 9780883850008 9780883859681 0883859688 |
| Source of Description, Etc. Note: | Print version record. |
