EMBEDDED H-PLANES IN HYPERBOLIC 3-SPACE

We show that for any C-0 Jordan curve Gamma in S-infinity(2)(H-3), there exists an embedded H-plane P-H in H-3 with partial derivative P-infinity(H) = Gamma for any H epsilon (-1, 1). As a corollary, we prove that any quasi-Fuchsian hyperbolic 3-manifold M similar or equal to Sigma x R contains an H-surface Sigma(H) in the homotopy class of the core surface Sigma for any H epsilon (-1, 1). We also prove that for any C-1 Jordan curve in S-infinity(2)(H-3), there exists a unique minimizing H-plane P-H with partial derivative P-infinity(H) = G for a generic H epsilon (-1, 1).