I am reading Masur's paper On a class of geodesic in Teichmuller space. He mentions that $T(S_0)$ where $S_0$ is a closed Riemann surface $g\geq2$ is straight, i.e. uniquely geodesic. It seems a well-known result, but as I am a beginner I am trying to prove it with the Teichmuller theorem at my disposal. Now I can prove that each $(k,\phi)$, where $k$ varies in $(-1,1)$ and $\phi$ is a fixed holomorphic quadratic differential, is a geodesic. But I don't know how to go on and prove that this is unique.

Also, the books/articles I've been reading point me to Kravetz's On the geometry of Teichmuller spaces and the structure of their modular group. But I can't find it anywhere online. Does anyone know where to look for this paper?

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    $\begingroup$ This follows from Teichmueller uniqueness. Abikoff's Real Analytic Theory of Teichmueller space has a proof in the last chapter. $\endgroup$ Nov 22, 2019 at 15:24


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