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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Extremal problems and symmetrization
for plane ring domains


Authors: A. Yu. Solynin and M. Vuorinen
Journal: Trans. Amer. Math. Soc. 348 (1996), 4095-4112
MSC (1991): Primary 30C85; Secondary 31A15
MathSciNet review: 1333399
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that Teichmüller's classical lower bound for the capacity of a ring domain, obtained by circular symmetrization, can be replaced by an explicit one which is almost always better. The proof is based on a duplication formula for the solution of an associated extremal problem. Some inequalities are obtained for conformal invariants.


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Additional Information

A. Yu. Solynin
Affiliation: Steklov Institute, Fontanka 27, St. Petersburg 191011, Russia
Email: solynin@pdmi.ras.ru FAX: 007-812-3105377

M. Vuorinen
Affiliation: University of Helsinki, FIN-00100 Helsinki, Finland
Email: vuorinen@csc.fi FAX: 358-0-1913213

DOI: http://dx.doi.org/10.1090/S0002-9947-96-01546-2
PII: S 0002-9947(96)01546-2
Received by editor(s): November 18, 1994
Received by editor(s) in revised form: May 2, 1995
Article copyright: © Copyright 1996 American Mathematical Society