Criteria for the divergence of pairs of Teichmüller geodesics

Anna Lenzhen (1) , Howard Masur (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Department of Mathematics

We study the asymptotic geometry of Teichmüller geodesic rays.We show that, when the transverse measures to the vertical foliations of the quadratic differentials determining two different rays are topologically equivalent, but are not absolutely continuous with respect to each other, the rays diverge in Teichmüller space.

Mots clés: Teichmüller space; Divergent geodesics; Extremal length; Ergodic

Anna Lenzhen, Howard Masur. Criteria for the divergence of pairs of Teichmüller geodesics. Geometriae Dedicata, 2010, 144 (1), pp.191-210. ⟨10.1007/s10711-009-9397-7⟩. ⟨hal-00695635⟩