A1 Refereed original research article in a scientific journal
Robin functions and distortion theorems for regular mappings
Authors: Dubinin V, Vuorinen M
Publication year: 2010
Journal: Mathematical News / Mathematische Nachrichten
Journal name in source: Mathematische Nachrichten
Number in series: 11
Volume: 283
Issue: 11
First page : 1589
Last page: 1602
Number of pages: 14
ISSN: 0025-584X
DOI: https://doi.org/10.1002/mana.200710143
Web address : http://api.elsevier.com/content/abstract/scopus_id:77958609710
Abstract
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.
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.
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