Uniformization Of Metric Surfaces Using Isothermal Coordinates

Toni Ikonen

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arXiv · 1909.09113

Uniformization Of Metric Surfaces Using Isothermal Coordinates

Toni Ikonen

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Abstract

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.

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Toni Ikonen. 2019-09-19. Uniformization Of Metric Surfaces Using Isothermal Coordinates. https://arxiv.org/abs/1909.09113

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