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Theory and practice of conformal geometry / Steven G. Krantz.

By: Material type: TextTextSeries: Aurora: Dover modern math originalsPublication details: Mineola, New York : Dover Publications, Inc., ©2016.Description: xii, 285 pages : illustrations ; 23 cmISBN:
  • 9780486793443
Subject(s): DDC classification:
  • 516.35 23 K89
Contents:
1. The Riemann mapping theorem -- 2. Invariant metrics -- 3. Normal families -- 4. Automorphism groups -- 5. The Schwarz Lemma -- 6. Harmonic measure -- 7. Extremal length -- 8. Analytic capacity -- 9. Invariant geometry -- 10. A new look at the Schwarz Lemma.
Summary: In this original text, prolific mathematics author Steven G. Krantz addresses conformal geometry, a subject that has occupied him for four decades and for which he helped to develop some of the modern theory. This book takes readers with a basic grounding in complex variable theory to the forefront of some of the current approaches to the topic. "Along the way," the author notes in his Preface, "the reader will be exposed to some beautiful function theory and also some of the rudiments of geometry and analysis that make this subject so vibrant and lively." More up-to-date and accessible to advanced undergraduates than most of the other books available in this specific field, the treatment discusses the hsitory of this active and popular branch of mathematics as well as recent developments. Topics include the Riemann mapping theorem, invariant metrics, normal families, automorphism groups, the Schwarz lemma, harmonic measure, extremal length, analytic capacity, and invariant geometry. A helpful Bibliography and Index complete the text.
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Includes bibliographical references and index.

1. The Riemann mapping theorem --
2. Invariant metrics --
3. Normal families --
4. Automorphism groups --
5. The Schwarz Lemma --
6. Harmonic measure --
7. Extremal length --
8. Analytic capacity --
9. Invariant geometry --
10. A new look at the Schwarz Lemma.

In this original text, prolific mathematics author Steven G. Krantz addresses conformal geometry, a subject that has occupied him for four decades and for which he helped to develop some of the modern theory. This book takes readers with a basic grounding in complex variable theory to the forefront of some of the current approaches to the topic. "Along the way," the author notes in his Preface, "the reader will be exposed to some beautiful function theory and also some of the rudiments of geometry and analysis that make this subject so vibrant and lively." More up-to-date and accessible to advanced undergraduates than most of the other books available in this specific field, the treatment discusses the hsitory of this active and popular branch of mathematics as well as recent developments. Topics include the Riemann mapping theorem, invariant metrics, normal families, automorphism groups, the Schwarz lemma, harmonic measure, extremal length, analytic capacity, and invariant geometry. A helpful Bibliography and Index complete the text.

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