# 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