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The Geometry of the Thurston Metric: A Survey

In: In the Tradition of Thurston III

Author

Listed:
  • Huiping Pan

    (South China University of Technology, School of Mathematics)

  • Weixu Su

    (Sun Yat-Sen University, School of Mathematics)

Abstract

This chapter is a survey about the Thurston metric on the Teichmüller space. The central issue is the construction of extremal Lipschitz maps between hyperbolic surfaces. We review several constructions, including the original work of Thurston. Coarse geometry and isometry rigidity of the Thurston metric, relation between the Thurston metric and the Thurston compactification are discussed. Some recent generalizations and developments of the Thurston metric are sketched.

Suggested Citation

  • Huiping Pan & Weixu Su, 2024. "The Geometry of the Thurston Metric: A Survey," Springer Books, in: Ken’ichi Ohshika & Athanase Papadopoulos (ed.), In the Tradition of Thurston III, chapter 0, pages 7-43, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-43502-7_2
    DOI: 10.1007/978-3-031-43502-7_2
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