Condenser Capacities and Symmetrization in Geometric Function Theory
Authors: Dubinin, Vladimir N.
Free Preview- First systematic presentation of the capacitory approach and symmetrization in complex analysis, the main part of which has not been covered by existing textbooks and monographs
- Valuable source for current and future researchers in various branches of complex analysis and potential theory
- Written by a well-known expert in geometric function theory and potential theory
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- About this book
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This is the first systematic presentation of the capacitory approach and symmetrization in the context of complex analysis. The content of the book is original – the main part has not been covered by existing textbooks and monographs. After an introduction to the theory of condenser capacities in the plane, the monotonicity of the capacity under various special transformations (polarization, Gonchar transformation, averaging transformations and others) is established, followed by various types of symmetrization which are one of the main objects of the book. By using symmetrization principles, some metric properties of compact sets are obtained and some extremal decomposition problems are solved. Moreover, the classical and present facts for univalent and multivalent meromorphic functions are proven.
This book will be a valuable source for current and future researchers in various branches of complex analysis and potential theory.
- Reviews
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“This is a very valuable book, both for students and researchers. The author is a world expert in symmetrization, polarization theory and geometric function theory. The book covers these topics in a systematic way, including some topics that never appeared in a book. … Useful exercises are given. I recommend the book for teaching these subjects without any hesitations.” (Dov Aharonov, zbMATH, Vol. 1305, 2015)
“This book is devoted to the capacitive approach and symmetrization methods in geometric function theory. The material comprises the extensive research carried out during the solution of several classical and modern problems of function theory and potential theory. … This book is warmly recommended to researchers and graduate students interested in function theory, potential theory, mathematical physics and related fields.” (Sergei Kalmykov, Acta Scientiarum Mathematicarum, Vol. 81 (1-2), 2015)
- Table of contents (8 chapters)
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Conformal Capacity
Pages 1-24
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The Asymptotic Behaviour of the Capacity as some Plates of the Condenser Degenerate into Points
Pages 25-60
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Special Transformations
Pages 61-87
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Symmetrization
Pages 89-121
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Metric Properties of Sets and Condensers
Pages 123-154
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Table of contents (8 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Condenser Capacities and Symmetrization in Geometric Function Theory
- Authors
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- Vladimir N. Dubinin
- Translated by
- Kruzhilin, N.G.
- Copyright
- 2014
- Publisher
- Birkhäuser Basel
- Copyright Holder
- Springer Basel
- eBook ISBN
- 978-3-0348-0843-9
- DOI
- 10.1007/978-3-0348-0843-9
- Hardcover ISBN
- 978-3-0348-0842-2
- Edition Number
- 1
- Number of Pages
- XII, 344
- Number of Illustrations
- 35 b/w illustrations
- Topics
