Abstract
Hamenstadt gave a parametrization of the Teichmuller space of punctured surfaces such that the image under this parametrization is the interior of a polytope. In this paper, we study the Hilbert metric on the Teichmuller space of punctured surfaces based on this parametrization. We prove that every earthquake ray is an almost geodesic under the Hilbert metric. Let Sg;n be an orientable surface of genus g with n punctures. In this paper, we consider the surfaces of negative Euler characteristic with at least one puncture. A marked hyperbolic structure on Sg;n is pair (X;f) where X is a complete hyperbolic metric on a surface S and f : Sg;n! S is a homeomorphism. Two marked hyperbolic structures (X1;f1) and (X1;f2) are called equivalent if there is an isometry in the
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