Lines of minima are uniformly quasigeodesic

Young-Eun Choi, Kasra Rafi and Caroline Series

Vol. 237 (2008), No. 1, 21–44

DOI: 10.2140/pjm.2008.237.21

Abstract

We continue the comparison between lines of minima and Teichmüller geodesics begun in our previous work. For two measured laminations ν⁺ and ν⁻ that fill up a hyperbolizable surface S and for t ∈ (−∞,∞), let ℒ_t be the unique hyperbolic surface that minimizes the length function e^tl(ν⁺) + e^−tl(ν⁻) on Teichmüller space. We prove that the path t↦ℒ_t is a Teichmüller quasigeodesic.

Keywords

lines of minima, Teichmüller space, quasigeodesic

Mathematical Subject Classification 2000

Primary: 30F60

Milestones

Received: 14 June 2007

Revised: 25 February 2008

Accepted: 10 March 2008

Published: 1 September 2008