Rigidity of Teichm\"uller space
Alex Eskin, Howard Masur, Kasra Rafi
TL;DR
This paper proves that Teichm"uller space exhibits quasi-isometric rigidity, meaning every quasi-isometry is close to an actual isometry, highlighting its geometric rigidity properties.
Contribution
It establishes the quasi-isometric rigidity of Teichm"uller space with the Teichm"uller metric, a significant geometric property not previously confirmed.
Findings
Every quasi-isometry of Teichm"uller space is close to an isometry.
Teichm"uller space is quasi-isometrically rigid.
Abstract
We prove that the every quasi-isometry of Teichm\"uller space equipped with the Teichm\"uller metric is a bounded distance from an isometry of Teichm\"uller space. That is, Teichm\"uller space is quasi-isometrically rigid.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAnalytic and geometric function theory · Geometric and Algebraic Topology · Holomorphic and Operator Theory