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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A circle packing measurable Riemann mapping theorem


Author: G. Brock Williams
Journal: Proc. Amer. Math. Soc. 134 (2006), 2139-2146
MSC (2000): Primary 52C26, 30F60
Published electronically: January 4, 2006
MathSciNet review: 2215785
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove a circle packing version of the Measurable Riemann Mapping Theorem in the spirit of Rodin and Sullivan's Circle Packing Riemann Mapping Theorem. We also construct circle packing maps of the plane onto itself with prescribed dilatation.


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Additional Information

G. Brock Williams
Affiliation: Department of Mathematics, Texas Tech University, Lubbock, Texas 79409
Email: williams@math.ttu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08200-1
PII: S 0002-9939(06)08200-1
Keywords: Circle packing, quasiconformal maps, Teichm\"uller theory
Received by editor(s): December 4, 2002
Received by editor(s) in revised form: February 10, 2005
Published electronically: January 4, 2006
Additional Notes: The author gratefully acknowledges the support of the Texas Tech University Research Enhancement Fund.
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.



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