EXTREMAL PROBLEMS and SYMMETRIZATION for PLANE RING DOMAINS

A. Y.U. Solynin; M. Vuorinen

doi:10.1090/s0002-9947-96-01546-2

EXTREMAL PROBLEMS and SYMMETRIZATION for PLANE RING DOMAINS

A. Y.U. Solynin, M. Vuorinen

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

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.

Original language	English
Pages (from-to)	4095-4112
Number of pages	18
Journal	Transactions of the American Mathematical Society
Volume	348
Issue number	10
DOIs	https://doi.org/10.1090/s0002-9947-96-01546-2
State	Published - 1996

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title = "EXTREMAL PROBLEMS and SYMMETRIZATION for PLANE RING DOMAINS",

abstract = "We show that Teichm{\"u}ller'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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AB - 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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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

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