Notes on Stable Teichmuller quasigeodesics

Abstract

In this note, we prove that for a cobounded,Lipschitz path $γ:I\to\TT$, if the pull back bundle ${\mathcal{H}}_{\gamma }$ over $I$ is a strongly relatively hyperbolic metric space then there exists a geodesic $\xi$ in $\TT$ such that $\gamma (I)$ and $\xi$ are close to each other.

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