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arXiv · 2103.16702

Non-compact Riemann surfaces are equilaterally triangulable

Christopher J. Bishop·Lasse Rempe
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Abstract

We show that every open Riemann surface can be obtained by glueing together a countable collection of equilateral triangles, in such a way that every vertex belongs to finitely many triangles. Equivalently, it is a _Belyi surface_: There exists a holomorphic branched covering to the Riemann sphere that is branched only over three values. It follows that every Riemann surface is a branched cover of the sphere, branched only over finitely many points.

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Christopher J. Bishop, Lasse Rempe. 2021-03-30. Non-compact Riemann surfaces are equilaterally triangulable. https://arxiv.org/abs/2103.16702

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