Limits of Teichmüller geodesics in the Universal Teichmüller space

Abstract

Thurston's boundary to the universal Teichmüller space $T(\mathbb{H})$ is the set of asymptotic rays to the embedding of $T(\mathbb{H})$ in the space of geodesic currents; the boundary is identified with the projective bounded measured laminations $PM{L}_{bdd}(\mathbb{H})$ of $\mathbb{H}$. We prove that each Teichmüller geodesic ray in $T(\mathbb{H})$ has a unique limit point in Thurston's boundary to $T(\mathbb{H})$ unlike in the case of closed surfaces.

23 pages, 6 figures, added reference

Cited by in corpus (1)

• A Thurston boundary for infinite-dimensional Teichmüller spaces