Thurston's asymmetric metric on Margulis spacetimes

2025/12/08 by Gongopadhyay, Krishnendu, Mondal, Neelanjan
Physics and Astronomy · Mathematics · #Advanced Differential Geometry Research #Analytic and geometric function theory #Geometric Analysis and Curvature Flows

paper · doi:10.48550/arxiv.2512.08019

Abstract

In this article, we extend Thurston's asymmetric metric and the associated Finsler norm, originally defined for Teichmüller space, to the setting of Margulis spacetimes. We also establish several convexity properties of both the asymmetric metric and the corresponding Finsler norm.

Citations

• The geometry of the Thurston metric: a survey
• Thurston's asymmetric metrics for Anosov representations
• Isospectrality of Margulis-Smilga spacetimes for irreducible representations of real split semisimple Lie groups
• Discrete isometry groups of symmetric spaces
• Some recent results on Anosov representations
• The pressure metric for Anosov representations
• Anosov Flows, Surface Groups and Curves in Projective Space
• Minimal stretch maps between hyperbolic surfaces

Related

• On the Finsler stucture of the Teichmüuller metric and Thurston's asymmetric metric
• Thurston's asymmetric metrics for Anosov representations
• Thurston's asymmetric metric for the space of flat metrics
• Tangent spaces of the Teichmüller space of the torus with Thurston's weak metric
• Convex bodies in Euclidean and Weil-Petersson geometries