The horoboundary and isometry group of Thurston's Lipschitz metric

Abstract

We show that the horofunction boundary of Teichmüller space with Thurston's Lipschitz metric is the same as the Thurston boundary. We use this to determine the isometry group of the Lipschitz metric, apart from in some exceptional cases. We also show that the Teichmüller spaces of different surfaces, when endowed with this metric, are not isometric, again with some possible exceptions of low genus.

23 pages, 5 figures. There was a mistake in one of the lemmas. Fixing it required replacing Lemmas 7.5, 7.6, and 7.7. The new version is very close to the published version

Cited by in corpus (15)

• Finsler bordifications of symmetric and certain locally symmetric spaces
• Central limit theorems for mapping class groups and $\text{Out}(F_N)$
• Coarse and fine geometry of the Thurston metric
• Gauge-reversing maps on cones, and Hilbert and Thompson isometries
• Polyhedral Horofunction Compactification as a Polyhedral Ball
• Automorphisms of graphs of cyclic splittings of free groups
• Generalized stretch lines for surfaces with boundary
• Characterizing the metric compactification of $L_p$ spaces by random measures
• Horofunction Compactifications of Symmetric Spaces
• Local Rigidity of Teichmüller space with Thurston metric
• Horofunction compactifications and duality
• A qualitative description of the horoboundary of the Teichmüller metric
• Optimal Lipschitz Maps on One-holed Tori and the Thurston Metric Theory of Teichmueller Space
• The infinitesimal and global Thurston geometry of Teichm{ü}ller space
• On continuity of drifts of the mapping class group