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Book Cover
E-book
Author Dubinin, V. N. (Vladimir Nikolaevich), author

Title Condenser capacities and symmetrization in geometric function theory / Vladimir N. Dubinin
Published Basel : Birkhäuser, 2014

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Description 1 online resource (xii, 344 pages) : illustrations
Contents Preface -- 1. Conformal capacity -- 2. Asymptotics of the condenser capacity when one of the plate degenerates -- Special transformations -- 4. Symmetrization -- 5. Metric properties of sets and condensers -- 6. Problems of extremal decomposition -- 7. Univalent functions -- 8. Multivalent functions -- Appendices: A1. Dirichlet principle -- A2. Uniqueness theorem for contracting mapping -- A3. On separating transformation of sets and condensers -- A4. On conservation of reduced moduli under geometric trans-formation of domains -- A5. Quadratic differentials -- A6. Unsolved problems -- References -- Basic notations -- Subject index
Summary 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
Analysis mathematische natuurkunde
mathematical physics
wiskunde
mathematics
Mathematics (General)
Wiskunde (algemeen)
Notes "Translated from the Russian by Nikolai G. Kruzhilin."
Bibliography Includes bibliographical references and index
Notes Online resource; title from PDF title page (SpringerLink, viewed August 29, 2014)
SUBJECT Kapazität gnd
Subject Mathematical physics.
SCIENCE -- Energy.
SCIENCE -- Mechanics -- General.
SCIENCE -- Physics -- General.
Mathematical physics
Geometrische Funktionentheorie
Symmetrisierung
Kondensator
Form Electronic book
Author Kruzhilin, Nikolai G., translator
ISBN 9783034808439
3034808437
3034808429
9783034808422