Lines of minima are uniformly quasi-geodesic

TL;DR

This paper proves that lines of minima in Teichmueller space are uniformly quasi-geodesic with respect to the Teichmueller metric, with constants depending only on the surface's topology.

Contribution

It establishes the quasi-geodesic property of lines of minima in Teichmueller space, extending previous comparisons with Teichmueller geodesics.

Findings

Lines of minima are quasi-geodesic in Teichmueller space.

Quasi-geodesic constants depend only on surface topology.

Extends previous comparison results between lines of minima and Teichmueller geodesics.

Abstract

We continue the comparison between lines of minima and Teichmueller geodesics begun in [CRS1]. We show that in the Teichmueller space of a surface S, lines of minima are quasi-geodesic with respect to the Teichmueller metric. The quasi-geodesic constants depend only on the topological type of S.