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Quasisymmetric parametrizations of two‐dimensional metric planes
Author(s) -
Wildrick K.
Publication year - 2008
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdn023
Subject(s) - uniformization (probability theory) , conformal map , equivalence (formal languages) , riemann hypothesis , mathematics , uniformization theorem , metric (unit) , riemann surface , combinatorics , algebra over a field , discrete mathematics , pure mathematics , geometry , geometric function theory , riemann–hurwitz formula , statistics , balance equation , operations management , markov model , markov chain , economics
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.