Uniformization of two-dimensional metric surfaces
Finna-arvio
Uniformization of two-dimensional metric surfaces
1412.3348v2.pdf
(Jyväskylän yliopisto - JYX)
We establish uniformization results for metric spaces that are homeomorphic to the Euclidean plane or sphere and have locally finite Hausdorff 2-measure. Applying the geometric definition of quasiconformality, we give a necessary and sufficient condition for such spaces to be QC equivalent to the Euclidean plane, disk, or sphere. Moreover, we show that if such a QC parametrization exists, then the dilatation can be bounded by 2. As an application, we show that the Euclidean upper bound for measures of balls is a sufficient condition for the existence of a 2-QC parametrization. This result gives a new approach to the Bonk-Kleiner theorem on parametrizations of Ahlfors 2-regular spheres by quasisymmetric maps.
Tallennettuna:
Kieli |
englanti |
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Sarja | Inventiones mathematicae, 3 |
Aiheet | |
ISSN |
0020-9910 |