Riemann Mapping Theorem

  • S. K. Singh


Riemann mapping theorem is one of the most important theorems in complex variables, and its proof utilizes almost all the important concepts of analytic functions. Before we state the theorem, let us recall some definitions. We shall use the symbol ℂ for the set of complex numbers and ℝ for the set of real numbers.


Open Subset Unit Disk Conformal Mapping Bergman Kernel Schwarz Lemma 


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  1. 1.
    Z. Nehari, “Conformai Mapping,” McGraw-Hill Book Co., New York, 1952.Google Scholar
  2. 2.
    B. Epstein, “Orthogonal Families of Analytic Functions,” Macmillan Co., New York, 1965.MATHGoogle Scholar

Copyright information

© Plenum Press 1968

Authors and Affiliations

  • S. K. Singh
    • 1
  1. 1.Karnatak UniversityDharwarIndia

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