  Almost-Fuchsian manifold is a class of complete hyperbolic three manifolds.
Such a three-manifold is a quasi-Fuchsian manifold which contains a closed
incompressible minimal surface with principal curvatures everywhere in the
range of (-1, 1). In such a manifold, the minimal surface is unique and
embedded, hence one can parametrize these hyperbolic three-manifolds by their
minimal surfaces. In this paper we obtain estimates on several geometric and
analytical quantities of an almost-Fuchsian manifold M in terms of the data on
the minimal surface. In particular, we obtain an upper bound for the hyperbolic
volume of the convex core of M, and an upper bound on the Hausdor? dimension of
the limit set associated to M. We also constructed a quasi-Fuchsian manifold
which admits more than one minimal surface, and it does not admit a foliation
of closed surfaces of constant mean curvature.
