Quasisymmetric parameterizations of two-dimensional metric planes

Details Quasisymmetric parameterizations of two-dimensional metric planes Quasisymmetric parameterizations of two-dimensional metric planes

2006-10-27

arxiv.org/abs/math/0610863v1

Mathematics

Metric Geometry

28 pages

Scientific paper

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.

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