Shearing coordinates and convexity of length functions on Teichmueller space

2009/02/05 by Mladen Bestvina, Bestvina, M., Kenneth Bromberg +5 · 3 citations
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.0902.0829

openalex publication_date 2009/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that there are Fenchel-Nielsen coordinates for the Teichmueller space of a finite area hyperbolic surface with respect to which the length functions are convex.

Citations

• Hyperbolic Structures on 3-manifolds, II: Surface groups and 3-manifolds which fiber over the circle

Cited by

• Bounding shears of spiralling triangulations on hyperbolic surfaces
• Understanding the well-rounded deformation retraction of Teichmüller space
• Schmutz-Thurston Duality

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