Robin functions and distortion theorems for regular mappings

: Dubinin V, Vuorinen M

: 2010

: Mathematical News / Mathematische Nachrichten

: Mathematische Nachrichten

: 11

: 283

: 11

: 1589

: 1602

: 14

: 0025-584X

DOI: https://doi.org/10.1002/mana.200710143

: http://api.elsevier.com/content/abstract/scopus_id:77958609710

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.