Affordable Access

The infinitesimal and global Thurston geometry of Teichmüller space

Authors
  • Huang, Yi
  • Ohshika, Ken'ichi
  • Papadopoulos, Athanase
Publication Date
Nov 25, 2021
Source
HAL
Keywords
Language
English
License
Unknown
External links

Abstract

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.

Report this publication

Statistics

Seen <100 times