Variation of the conformal radius |
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| Authors: | Steffen Rohde Michel Zinsmeister |
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| Institution: | (1) Department of Mathematics, University of Washington, Box 354350, 98195-4350 Seattle, WA, USA;(2) MAPMO, Département de mathématiques, Université d'Orléans, B.P. 6759, 45067 Orléans Cedex 2, France |
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| Abstract: | We study the change of the conformal radiusr(U) of a simply connected planar domainU versus the subdomainU
ε consisting of the points of distance at least ε to ∂U. We show that the smallest exponent λ such thatr(U)-r(U
t)=0(e
λ) satisfies 0.59<λ<0.91. We also show that a well-known conjecture implies
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Partially supported by NSF Grant DMS-9970398. |
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