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Robin functions and distortion theorems for regular mappings
Author(s) -
Dubinin V. N.,
Vuorinen M.
Publication year - 2010
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200710143
Subject(s) - mathematics , distortion (music) , conformal map , domain (mathematical analysis) , boundary (topology) , function (biology) , point (geometry) , pure mathematics , mathematical analysis , geometry , computer science , computer network , amplifier , bandwidth (computing) , evolutionary biology , biology
Capacities of generalized condensers are applied to prove a two‐point distortion theorem for conformal mappings. The result is expressed in terms of the Robin function and the Robin capacity with respect to the domain of definition of the mapping and subsets of the boundary of this domain. The behavior of Robin function under multivalent functions is studied. Some corollaries and examples of applications to distortion theorems for regular functions are given (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)