The infinitesimal and global Thurston geometry of Teichmüller space

Yi Huang YMSC, Tsinghua University Ken'ichi Ohshika Gakushuin University Athanase Papadopoulos IRMA, University of Strasbourg

Differential Geometry Geometric Analysis and Geometric Topology arXiv subject: Differential Geometry (math.DG) mathscidoc:2206.10003

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.
rigidity, infinitesimal rigidity, Thurston metric, Teichmueller theory, hyperbolic surfaces, Lipschitz homeomorphisms
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  • preprint, currently under review
@inproceedings{yithe,
  title={The infinitesimal and global Thurston geometry of Teichmüller space},
  author={Yi Huang, Ken'ichi Ohshika, and Athanase Papadopoulos},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220608153031359384345},
}
Yi Huang, Ken'ichi Ohshika, and Athanase Papadopoulos. The infinitesimal and global Thurston geometry of Teichmüller space. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220608153031359384345.
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