Bounded ideal triangulations of infinite Riemann surfaces

Casey Whitney; Dragomir Saric

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arXiv · 2502.05590

Bounded ideal triangulations of infinite Riemann surfaces

Casey Whitney·Dragomir Saric

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Abstract

We introduce a notion of a bounded ideal triangulation of an infinite Riemann surface and parametrize Teichm\"uller spaces of infinite surfaces which allow bounded triangulations. We prove that our parametrization is real-analytic. Riemann surfaces with bounded geometry and countably many punctures belong to the class of surfaces with bounded ideal triangulations. In comparison, the Fenchel-Nielsen parametrization for surfaces with bounded geometry is not known, while the Fenchel-Nielsen parametrization for surfaces with bounded pants decompositions is known as a homeomorphism but it is not known whether it is real-analytic

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Casey Whitney, Dragomir Saric. 2025-02-08. Bounded ideal triangulations of infinite Riemann surfaces. https://arxiv.org/abs/2502.05590

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