Huiping Pan, Weixu Su
Published 2023-07-08Version 1
This paper is a survey about the Thurston metric on the Teichm\"uller space. The central issue is the constructions 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.
Comments: 42 pages. This article will appear as a chapter in the book: In the tradition of Thurston, III (ed. K. Ohshika and A. Papadopoulos), Springer Verlag
Envelopes of the Thurston metric on Teichmüller space
Prime orthogeodesics, concave cores and families of identities on hyperbolic surfaces
Coarse and fine geometry of the Thurston metric
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