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Rigidity of Teichmüller space

Alex Eskin, Howard Masur and Kasra Rafi
Geometry & Topology 22 (2018) 4259–4306
DOI: 10.2140/gt.2018.22.4259
Abstract

We prove that every quasi-isometry of Teichmüller space equipped with the Teichmüller metric is a bounded distance from an isometry of Teichmüller space. That is, Teichmüller space is quasi-isometrically rigid.

Keywords
quasi-isometric rigidity, Teichmüller metric
Mathematical Subject Classification 2010
Primary: 32G15
References
Publication
Received: 6 October 2017
Accepted: 23 April 2018
Published: 6 December 2018
Proposed: Benson Farb
Seconded: Tobias H Colding, Jean-Pierre Otal
Authors
Alex Eskin
Department of Mathematics
University of Chicago
Chicago, IL
% 60637-1514
United States
Howard Masur
Department of Mathematics
University of Chicago
Chicago, IL
% 60637-1514
United States
Kasra Rafi
Department of Mathematics
University of Toronto
Toronto, ON
% M5S 2E4
Canada