| Résume | The geodesic flow in negative curvature is a beautiful and well-studied topic in geometry. I will introduce an analogy between geodesics, which are one-dimensional minimal surfaces, and two-dimensional minimal surfaces in negatively curved 3-manifolds, based on recent work of Calegari-Marques-Neves. I will also talk about area lower bounds for certain minimal surfaces in closed riemannian 3-manifolds M with a negative scalar curvature lower bound, that hold if M has a hyperbolic metric. These lower bounds improve the lower bounds from the second variation formula, and are proved using the Ricci flow with surgery. |
