Masur's criterion does not hold in the Thurston metric

2019/03/03 by Telpukhovskiy, Ivan
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1903.00845

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 λ 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 λ, stays in the thick part for the whole time.

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