Bounding shears of spiralling triangulations on hyperbolic surfaces

2025/12/10 by Abadie, Marie
#30F60 #57M50 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2512.09818

Abstract

We show that all hyperbolic surfaces admit an ideal triangulation with bounded shear parameters. This upper bound depends logarithmically on the topology of the surface.

Citations

• Quantifying the sparseness of simple geodesics on hyperbolic surfaces
• Interrogating surface length spectra and quantifying isospectrality
• Shearing coordinates and convexity of length functions on Teichmueller space
• On Quantizing Teichmüller and Thurston theories
• Minimal stretch maps between hyperbolic surfaces

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• Circular foliations and shear-radius coordinates on Teichmüller spaces of hyperbolic cone surfaces
• Minimal Delaunay triangulations of hyperbolic surfaces
• Random ideal triangulations and the Weil-Petersson distance between finite degree covers of punctured Riemann surfaces
• Pseudo-Developing Maps for Ideal Triangulations I: Essential Edges and Generalised Hyperbolic Gluing Equations