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Quasiconformal variation of slit domains


Authors: Clifford J. Earle and Adam Lawrence Epstein
Journal: Proc. Amer. Math. Soc. 129 (2001), 3363-3372
MSC (2000): Primary 30C20, 30C62
Published electronically: January 29, 2001
MathSciNet review: 1845014
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Abstract | References | Similar Articles | Additional Information

Abstract:

We use quasiconformal variations to study Riemann mappings onto variable single slit domains when the slit is the tail of an appropriately smooth Jordan arc. In the real analytic case our results answer a question of Dieter Gaier and show that the function $\kappa$ in Löwner's differential equation is real analytic.


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Additional Information

Clifford J. Earle
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
Email: cliff@math.cornell.edu

Adam Lawrence Epstein
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
Address at time of publication: Department of Mathematics, University of Warwick, Coventry CV4 7AL, England
Email: adame@math.cornell.edu, adame@maths.warwick.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-01-05991-3
Keywords: Conformal radius, slit domain, L\"owner differential equation
Received by editor(s): January 27, 2000
Received by editor(s) in revised form: March 24, 2000
Published electronically: January 29, 2001
Additional Notes: The second author was supported in part by NSF Grant DMS 9803242.
Communicated by: Albert Baernstein II
Article copyright: © Copyright 2001 American Mathematical Society