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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Extremal problems and symmetrization for plane ring domains
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by A. Yu. Solynin and M. Vuorinen PDF
Trans. Amer. Math. Soc. 348 (1996), 4095-4112 Request permission

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
  • MR Author ID: 206458
  • Email: solynin@pdmi.ras.ru FAX: 007-812-3105377
  • M. Vuorinen
  • Affiliation: University of Helsinki, FIN-00100 Helsinki, Finland
  • MR Author ID: 179630
  • Email: vuorinen@csc.fi FAX: 358-0-1913213
  • Received by editor(s): November 18, 1994
  • Received by editor(s) in revised form: May 2, 1995
  • © Copyright 1996 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 348 (1996), 4095-4112
  • MSC (1991): Primary 30C85; Secondary 31A15
  • DOI: https://doi.org/10.1090/S0002-9947-96-01546-2
  • MathSciNet review: 1333399