• Published 2008

1 9 Se p 20 02 Hyperbolic manifolds with convex boundary

@inproceedings{Schlenker200819S,
  title={1 9 Se p 20 02 Hyperbolic manifolds with convex boundary},
  author={Jean-Marc Schlenker},
  year={2008}
}
Let (M, ∂M) be a 3-manifold, which carries a hyperbolic metric with convex boundary (but is not a solid torus). We consider the hyperbolic metrics on M such that the boundary is smooth and strictly convex. We show that the induced metrics on the boundary are exactly the metrics with curvature K > −1, and that the third fundamental forms of ∂M are exactly the metrics with curvature K < 1, for which contractible closed geodesics have length L > 2π. Each is obtained exactly once. Other related… CONTINUE READING

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