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<p>The Riemann mapping theorem states that a simply connected proper subregion of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\mathbb {C}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">C</mi> </math></EquationSource> </InlineEquation> is conformally equivalent to the hyperbolic plane. We give a proof of the Riemann mapping theorem that is based on the hyperbolic metric.</p>

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The Hyperbolic Metric and the Riemann Mapping Theorem

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月23日

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  • A. F. Beardon

摘要

The Riemann mapping theorem states that a simply connected proper subregion of \({\mathbb {C}}\) C is conformally equivalent to the hyperbolic plane. We give a proof of the Riemann mapping theorem that is based on the hyperbolic metric.