Uniformization Of Metric Surfaces Using Isothermal Coordinates

We establish a uniformization result for metric surfaces - metric spaces that are topological surfaces with locally finite Hausdorff 2-measure. Using the geometric definition of quasiconformality, we show that a metric surface that can be covered by quasiconformal images of Euclidean domains is quas...

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Bibliographic Details
Published in:arXiv.org 2019-09
Main Author: Ikonen, Toni
Format: Article
Language:English
Subjects:
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Euclidean geometry
Riemann surfaces
Online Access:Get full text
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Summary:We establish a uniformization result for metric surfaces - metric spaces that are topological surfaces with locally finite Hausdorff 2-measure. Using the geometric definition of quasiconformality, we show that a metric surface that can be covered by quasiconformal images of Euclidean domains is quasiconformally equivalent to a Riemannian surface. To prove this, we construct suitable isothermal coordinates.
ISSN:2331-8422