The Hyperbolic Metric and the Riemann Mapping Theorem
Abstract The Riemann mapping theorem states that a simply connected proper subregion of $${\mathbb {C}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>C</mml:mi> </mml:math> is conformally equivalent to the hyperbolic plane. We give a proof of the Riemann mapping theorem that is based on the hyperbolic metric.
Authors
- A. F. Beardon
Publication Details
- Journal
- Computational Methods and Function Theory
- Published
- 2025-04-23
- DOI
- https://doi.org/10.1007/s40315-025-00584-5
- Primary Topic
- Algebraic and Geometric Analysis
- Type
- article
- Field-Weighted Citation Impact
- 0.00