The Geometry of the Thurston Metric: A Survey

Huiping Pan () and Weixu Su ()
Additional contact information
Huiping Pan: South China University of Technology, School of Mathematics
Weixu Su: Sun Yat-Sen University, School of Mathematics

Chapter Chapter 2 in In the Tradition of Thurston III, 2024, pp 7-43 from Springer

Abstract: 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.

Keywords: Teichmüller space; Thurston metric; Hyperbolic surfaces; Lipschitz maps; Harmonic maps; Thurston boundary; Isometry rigidity; Shearing coordinates; 32G15; 30F45; 30F60 (search for similar items in EconPapers)
Date: 2024
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-43502-7_2

Ordering information: This item can be ordered from
http://www.springer.com/9783031435027

DOI: 10.1007/978-3-031-43502-7_2

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().