Minimal Surfaces in Negatively Curved 3-Manifolds and Dynamics

Abstract: The Grassmann bundle of tangent 2-planes over a closed hyperbolic 3-manifold M has a natural foliation by (lifts by their tangent planes of) immersed totally geodesic planes in M. I am going to talk about work I’ve done on constructing foliations whose leaves are (lifts of) minimal surfaces in a metric on M of negative sectional curvature, which are deformations of the totally geodesic foliation described above. These foliations make it possible to use homogeneous dynamics to study how closed minimal surfaces in variable negative curvature are distributed in the ambient 3-manifold. Many of the ideas here come from recent work of Calegari-Marques-Neves, which I will also talk about. I was able to establish some preliminary facts about the dynamics of these foliations, but much remains to be understood.

differential geometry

Audience: researchers in the topic

Pangolin seminar

Series comments: TIME HAS CHANGED: 15:30 Paris 10:30AM Rio de Janeiro

Description: Differential geometry seminar

Zoom link posted on the webpage 15 minutes before each lecture: https://sites.google.com/view/pangolin-seminar/home