COUNTING MINIMAL SURFACES IN QUASI-FUCHSIAN THREE-MANIFOLDS

It is well known that every quasi-Fuchsian manifold admits at least one closed incompressible minimal surface, and at most finitely many stable ones. In this paper, for any prescribed integer N > 0, we construct a quasi-Fuchsian manifold which contains at least 2(N) such minimal surfaces. As a consequence, there exists some simple closed Jordan curve on S-infinity(2) such that there are at least 2(N) disk-type complete minimal surfaces in H-3 sharing this Jordan curve as the asymptotic boundary.