6533b85bfe1ef96bd12baa21
RESEARCH PRODUCT
Uniformization of metric surfaces using isothermal coordinates
Toni Ikonensubject
Mathematics - Complex VariablesMathematics::Complex VariablesPrimary 30L10 Secondary 30C65 28A75 51F99 52A38Metric Geometry (math.MG)ArticlesreciprocalityuniformizationisothermalMathematics - Metric GeometryQuasiconformalFOS: Mathematicssurfaceapproximate metric differentialComplex Variables (math.CV)description
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2021-12-13 |