Overview

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.

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9783034808422

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From the book reviews: 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)

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