The infinitesimal and global Thurston geometry of Teichmüller space

Yi Huang (1) , Ken'Ichi Ohshika (2) , Athanase Papadopoulos (3)

1 Yau Mathematical Sciences Center, Tsinghua University, Beijing
2 Department of Mathematics [Gakushuin]
3 IRMA - Institut de Recherche Mathématique Avancée

We undertake a systematic study of the infinitesimal geometry of the Thurston metric, showing that the topology, convex geometry and metric geometry of the tangent and cotangent spheres based at any marked hyperbolic surface representing a point in Teichmüller space can recover the marking and geometry of this marked surface. We then translate the results concerning the infinitesimal structures to global geometric statements for the Thurston metric, most notably deriving rigidity statements for the Thurston metric analogous to the celebrated Royden theorem.

Mots clés: stretch map; convex geometry; hyperbolic surfaces; rigidity; Thurston metric; Teichmüller space

Domaines: Topologie géométrique [math.GT]; Géométrie métrique [math.MG]

Yi Huang, Ken'Ichi Ohshika, Athanase Papadopoulos. The infinitesimal and global Thurston geometry of Teichmüller space. 2024. ⟨hal-03449425v3⟩