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Let $S_{g,n}$ be a surface of genus $g > 1$ with $n>0$ punctures equipped with a complete hyperbolic cusp metric.
Existence of a convex polyhedron and of a convex surface with a given metric
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The decorated Teichmüller space of punctured surfaces
R. C. Penner · 1987
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D. B. A. Epstein and R. C. Penner · 1988
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