16 jun 2026 -- 14:30
Dipartmento di Matematica "Giuseppe Peano", Università di Torino
Abstract.
Quasi-Fuchsian groups have been the subject of extensive study since the 1890s. By naturally acting on 3-dimensional hyperbolic space, they describe a wide class of complete, infinite-volume hyperbolic 3-manifolds. Their properties have played a crucial role in Thurston's hyperbolization theorem and, more generally, in the study of the geometry and topology of 3-manifolds. Following Uhlenbeck, we say that a quasi-Fuchsian manifold is almost-Fuchsian if it contains an incompressible minimal surface with principal curvatures between -1 and 1. A conjecture by Thurston asserts that any almost-Fuchsian manifold admits a foliation by constant mean curvature (CMC) surfaces. In this talk, I will describe a result from an upcoming joint work with Tien Nguyen, Andrea Seppi, and Jean-Marc Schlenker, where we determine explicit conditions on the first and second fundamental forms of the minimal surface of an almost-Fuchsian manifold that guarantee the existence of a CMC foliation.