Canonical domains on Riemann surfaces

Maskit, Bernard

doi:10.1090/S0002-9939-1989-0964458-7

Canonical domains on Riemann surfaces
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Proc. Amer. Math. Soc. 106 (1989), 713-721 Request permission

Abstract:

Let $S$ be a Riemann surface of genus $g > 0$, and of finite topological type. Then $S$ can be uniquely realized as a closed Riemann surface from which a finite number of disjoint points and closed circular discs have been removed. As a corollary, we obtain that the moduli space of surfaces of genus $g$ with one hole is a topological product of the moduli space of surfaces of genus $g$ with one puncture and an interval.

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Die Werte des Doppelverhältnisses bei schlichter konformer Abbildung

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