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Proceedings of the London Mathematical Society Advance Access published online on May 2, 2008
Proceedings of the London Mathematical Society, doi:10.1112/plms/pdn023
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© 2008 London Mathematical Society

Quasisymmetric parametrizations of two-dimensional metric planes

K. Wildrick

Department of Mathematics
University of Michigan
530 Church Street
Ann Arbor, MI 48109
USA

Received 11 September 2006. Revision received 22 June 2007.

The classical uniformization theorem states that any simply connected Riemann surface is conformally equivalent to the disk, the plane, or the sphere, each equipped with a standard conformal structure. We give a similar uniformization for Ahlfors 2-regular, linearly locally connected metric planes; instead of conformal equivalence, we are concerned with quasisymmetric equivalence.

The author was partially supported by NSF grants DMS-0200566, DMS-0244421, and RTG- 0602191.

2000 Mathematics Subject Classification 30C65.


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