Convexity of geodesic-length functions: a reprise

2005/02/24 by Scott A. Wolpert, Wolpert, Scott A. · 2 citations
Mathematics · Medicine · #30F60 #32G15 #53C22 #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Pharmacological Effects of Medicinal Plants #Point processes and geometric inequalities #math.DG #msc:30F60 #msc:32G15 #msc:53C22

paper · pdf · doi:10.48550/arxiv.math/0502526

14 pages

arxiv created 2005/02/24 · openalex publication_date 2005/02/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

New results on the convexity of geodesic-length functions on Teichmüller space are presented. A formula for the Hessian of geodesic-length is presented. New bounds for the gradient and Hessian of geodesic-length are described. A relationship of geodesic-length functions to Weil-Petersson distance is described. Applications to the behavior of Weil-Petersson geodesics are discussed.

Cited by

• Adapted Renormalized Volume for Hyperbolic 3-Manifolds with Compressible Boundary
• Harmonic Maps and Teichmueller Theory

Related

• The Weil-Petersson Hessian of Length on Teichmuller Space
• Length of a curve is quasi-convex along a Teichmuller geodesic
• Convexity of length functions and Thurston's shear coordinates
• Behavior of geodesic-length functions on Teichmueller space
• Variation of geodesic length functions over Teichmüller space