Quasisymmetric parameterizations of two-dimensional metric planes

Abstract

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.

28 pages

References in corpus (2)

• Conformal dimension and Gromov hyperbolic groups with 2-sphere boundary
• The branch set of a quasiregular mapping

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• Porosity of the branch set of discrete open mappings with controlled linear dilatation
• Quasisymmetric structures on surfaces
• Sphericalization and flattening with their applications in quasimetric measure spaces
• Quasiconformal non-parametrizability of almost smooth spheres
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• Preserving Besov (fractional Sobolev) energies under sphericalization and flattening
• Sphericalization with its applications in Gromov hyperbolic spaces
• Geometry and quasisymmetric parametrization of Semmes spaces