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Condenser capacities and symmetrization in geometric function theory. Translated from the Russian by Nikolai G. Kruzhilin. (English) Zbl 1305.30002

Basel: Birkhäuser/Springer (ISBN 978-3-0348-0842-2/hbk; 978-3-0348-0843-9/ebook). xii, 344 p. (2014).
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. For instance polarization is presented very nicely as well as reduced moduli. The quadratic differential is presented clearly as well. Useful exercises are given. I recommend the book for teaching these subjects without any hesitations.

MSC:

30-02 Research exposition (monographs, survey articles) pertaining to functions of a complex variable
30C85 Capacity and harmonic measure in the complex plane
31C15 Potentials and capacities on other spaces
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