Quasisymmetric parameterizations of two -dimensional metric spaces.

The classical Uniformization Theorem states that every simply connected Riemann surface is conformally equivalent to one of the disk, the plane, and the sphere, each equipped with a standard conformal structure. We give a similar classification for Ahlfors 2-regular, LLC simply connected metric surfaces; instead of conformal maps, we are interested in quasisymmetric maps. We also show that locally Ahlfors 2-regular and linearly locally contractible metric surfaces have a quasisymmetric atlas.Ph.D.MathematicsPure SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/126854/2/3276328.pd