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A family of coordinates $psi_h$ for the Teichmuller space of a compact surface with boundary was introduced in cite{l2}. In the work cite{m1}, Mondello showed that the coordinate $psi_0$ can be used to produce a natural cell decomposition of the Teichmuller space invariant under the action of the mapping class group. In this paper, we show that the similar result also works for all other coordinate $psi_h$ for any $h geq 0$.
Let $X_{0}$ be a complete hyperbolic surface of infinite type with geodesic boundary which admits a countable pair of pants decomposition. As an application of the Basmajian identity for complete bordered hyperbolic surfaces of infinite type with lim
We prove that the length spectrum metric and the arc-length spectrum metric are almost-isometric on the $epsilon_0$-relative part of Teichmuller spaces of surfaces with boundary.
We prove that the Teichmuller space of surfaces with given boundary lengths equipped with the arc metric (resp. the Teichmuller metric) is almost isometric to the Teichmuller space of punctured surfaces equipped with the Thurston metric (resp. the Teichmuller metric).
We investigate the translation lengths of group elements that arise in random walks on weakly hyperbolic groups. In particular, without any moment condition, we prove that non-elementary random walks exhibit at least linear growth of translation leng
We study the convergence of earthquake paths and horocycle paths in the Gardiner-Masur compactification of Teichmuller space. We show that an earthquake path directed by a uniquely ergodic or simple closed measured geodesic lamination converges to th