Large embedded balls and Heegaard genus in negative curvature.
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Bachman, David, Cooper, Daryl, White, Matthew E. (2004)
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Cooper, D., Long, D.D. (2001)
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Minsky, Yair N. (2000)
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François Fillastre (2007)
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A Fuchsian polyhedron in hyperbolic space is a polyhedral surface invariant under the action of a Fuchsian group of isometries (i.e. a group of isometries leaving globally invariant a totally geodesic surface, on which it acts cocompactly). The induced metric on a convex Fuchsian polyhedron is isometric to a hyperbolic metric with conical singularities of positive singular curvature on a compact surface of genus greater than one. We prove that these metrics are actually realised by exactly...
Francis Bonahon (1996)
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Michael Kapovich, Bruce Kleiner (2000)
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