Masur's criterion does not hold in the Thurston metric

Abstract

We construct a counterexample for an analogue of Masur's criterion in the setting of Teichmüller space equipped with the Thurston metric. For that, we find a minimal, filling, non-uniquely ergodic lamination $\lambda$ on the seven-times punctured sphere with uniformly bounded annular projection distances. Then we show that a geodesic in the corresponding Teichmüller space that converges to $\lambda$, stays in the thick part for the whole time.

arXiv comment29 pages, 18 figures. Completely rewritten following the referee's comments