10/12: Ben Lowe

Abstract:  The Grassmann bundle of tangent 2-planes over a closed hyperbolic 3-manifold M has a natural foliation by (lifts 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. The foliations we construct 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.  I was able to prove some preliminary results on the dynamics of these foliations, but much remains to be understood.