The classical Lindelöf principle on the behavior of Green’s function under a regular mapping is generalized to the case of Robin function with a pole at a boundary point. In addition, inequalities inverse to the Lindelöf principle are considered. As corollaries, certain analogs of Mityuk’s theorems on the behavior of the inner radius of a domain are established. Also a particular case of a Mityuk’s theorem and a Kloke’s result on the change of the condenser capacity under a multivalent mapping are supplemented. Bibliography: 19 titles.
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Dedicated to my teaher, Igor' Petrovich Mityuk
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 371, 2009, pp. 37–55.
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Dubinin, V.N. On I. P. Mityuk’s results on the behavior of the inner radius of a domain and the condenser capacity under regular mappings. J Math Sci 166, 145–154 (2010). https://doi.org/10.1007/s10958-010-9854-8
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DOI: https://doi.org/10.1007/s10958-010-9854-8