Thurston's metric on Teichmüller space and homeomorphisms between Fuchsian groups

Athanase Papadopoulos (1) , Weixu Su (2)

1 IRMA - Institut de Recherche Mathématique Avancée
2 Fudan University

In this paper, we establish relations between Thurston's metric on Teichmüller space and the work of T. Sorvali on isomorphisms between Fuchsian groups. As a result, we obtain a new formula for Thurston's metric for surfaces with punctures. We also upade some results of Sorvali on boundary isomorphisms of Fuchsian groups.

Mots clés: Thurston's metric; Fuchsian group; translation length; Teichmüller space; boundary mapping.

Domaines: Topologie géométrique [math.GT]; Variables complexes [math.CV]

Athanase Papadopoulos, Weixu Su. Thurston's metric on Teichmüller space and homeomorphisms between Fuchsian groups. Analysis and Geometry of Discrete Groups and Hyperbolic Spaces, B48, Research Institute for Mathematical Sciences, pp.95-110, 2014, RIMS Kôkyûroku Bessatsu. ⟨hal-01109088⟩