Abstract

Talk 1

Title: CMC foliations and Hamiltonian flows for quasi-Fuchsian manifolds.

Abstract: Quasi-Fuchsian are an important class of hyperbolic three-manifolds. In this talk I will present several results, obtained in a joint work with Diptaishik Choudhury and Filippo Mazzoli, on their foliations by constant mean curvature (CMC) surfaces. A conjecture due to Thurston asserts that every almost-Fuchsian manifold has a global CMC foliation: in the first part of the talk I will present a partial result in this direction, namely that every quasi-Fuchsian manifold in a neighbourhood of the Fuchsian locus is foliated by CMC surfaces. In the second part of the talk I will then explain how these CMC foliations induce Hamiltonian flows on the cotangent bundle of the Teichmüller space, and give some elements of the proof.

Talk 2

Title: Hyperbolic planes in three-dimensional Minkowski space.

Abstract: It is well-known that the hyperboloid is an isometrically embedded copy of the hyperbolic plane in Minkowski space; in 1983 Hano and Nomizu provided examples of other, non-equivalent, isometric embeddings of the hyperbolic plane. In this talk, we will discuss the question of classifying all such isometric embeddings, which is still open in full generality, and generalize some of the results to complete surfaces of bounded negative curvature. This is joint work with Francesco Bonsante and Peter Smillie.