Tien Nguyen (Luxembourg) will speak in the geometry seminar at 2pm on 31st March, in the Salle des Profs (9th floor of building NO). Tien’s title is “Minimal and CMC surfaces in hyperbolic 3-manifolds” and his abstract is below.
Let M be a 3-manifold of the form \Sigma \times (-1,1). The first goal of this talk is to discuss the role of minimal surfaces and surfaces of small curvature in the hyperbolic geometry of M. The second goal is to introduce a correspondence, due to V. Moncrief, between foliations of M by surfaces of constant-mean-curvature (CMC) and flow lines of a Hamiltonian system in the cotangent of the Teichmüller space of $\Sigma$. If time permits, I will present a long-time existence result for this flow, which guarantees the existence of CMC foliation for a certain class of quasi-Fuchsian manifolds.