An extremal decomposition problem for harmonic measure

Authors:
Vladimir N. Dubinin and Matti Vuorinen

Journal:
Proc. Amer. Math. Soc. **140** (2012), 2441-2446

MSC (2010):
Primary 30C85

Published electronically:
November 17, 2011

MathSciNet review:
2898706

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a continuum in the closed unit disk of the complex -plane which divides the open disk into pairwise nonintersecting simply connected domains such that each of the domains contains some point on a prescribed circle , It is shown that for some increasing function independent of and the choice of the points the mean value of the harmonic measures

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Additional Information

**Vladimir N. Dubinin**

Affiliation:
Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences, Vladivostok, Russia

Email:
dubinin@iam.dvo.ru

**Matti Vuorinen**

Affiliation:
Department of Mathematics, University of Turku, Turku 20014, Finland

Email:
vuorinen@utu.fi

DOI:
https://doi.org/10.1090/S0002-9939-2011-11109-2

Keywords:
Harmonic measure,
inner radius,
extremal decomposition.

Received by editor(s):
December 4, 2010

Received by editor(s) in revised form:
January 6, 2011, and February 24, 2011

Published electronically:
November 17, 2011

Additional Notes:
The research of the first author was supported by the Far-Eastern Branch of the Russian Academy of Sciences, project 09-III-A-01-007

The second author was supported by the Academy of Finland, project 2600066611

Communicated by:
Mario Bonk

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.