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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