Condenser Capacities and Symmetrization in Geometric Function Theory

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.

"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)