Condenser Capacities and Symmetrization in Geometric Function Theory

  • Vladimir N. Dubinin

Table of contents

  1. Front Matter
    Pages i-xii
  2. Vladimir N. Dubinin
    Pages 1-24
  3. Vladimir N. Dubinin
    Pages 61-87
  4. Vladimir N. Dubinin
    Pages 89-121
  5. Vladimir N. Dubinin
    Pages 123-154
  6. Vladimir N. Dubinin
    Pages 155-199
  7. Vladimir N. Dubinin
    Pages 201-275
  8. Vladimir N. Dubinin
    Pages 277-304
  9. Back Matter
    Pages 305-344

About this book


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.


condenser capacities extremal decomposition problems multivalent functions symmetrization univalent functions

Authors and affiliations

  • Vladimir N. Dubinin
    • 1
  1. 1.Institute of Applied MathematicsFar Eastern Federal UniversityVladivostokRussia

Bibliographic information