Lines of minima are uniformly quasigeodesic

Abstract

We continue the comparison between lines of minima and Teichmuller geodesics begun in our previous work. For two measured laminations nu(+) and nu(-) that fill up a hyperbolizable surface S and for t is an element of (-infinity, infinity), let L-t be the unique hyperbolic surface that minimizes the length function e(t) l(nu(+)) + e(-t) l(nu(-)) on Teichmuller space. We prove that the path t bar right arrow L-t is a Teichmuller quasigeodesic.