The Hilbert metric on Teichm\"uller space and Earthquake

Huiping Pan

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arXiv · 1703.02683

The Hilbert metric on Teichm\"uller space and Earthquake

Huiping Pan

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Abstract

Hamenst\"adt gave a parametrization of the Teichm\"uller 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 Teichm\"uller space of punctured surfaces based on this parametrization. We prove that every earthquake ray is an almost geodesic under the Hilbert metric.

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Huiping Pan. 2017-03-08. The Hilbert metric on Teichm\"uller space and Earthquake. https://arxiv.org/abs/1703.02683

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