  We show that for any C^0 Jordan curve C in the sphere at infinity of H^3,
there exists an embedded $H$-plane P_H in H^3 with asymptotic boundary C for
any H in (-1,1). As a corollary, we proved that any quasi-Fuchsian hyperbolic
3-manifold M=SxR contains an H-surface S_H in the homotopy class of the core
surface S for any H in (-1,1). We also proved that for any C^1 Jordan curve J
in the sphere at infinity, there exists a unique minimizing H-plane P_H with
asymptotic boundary J for a generic H in (-1,1).
