Notes on Stable Teichmuller quasigeodesics

In this note, we prove that for a cobounded,Lipschitz path $\gamma:I\to\TT$, 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.