Thesis defense
Keaton Quinn
UIC
Limits of Foliations in Quasi-Fuchsian Manifolds
Abstract: We introduce the notion of an asymptotically Poincaré family of surfaces in an end of a quasi-Fuchsian manifold. We show that any such family gives a foliation of an end by asymptotically parallel convex surfaces, and that the asymptotic behavior of the first and second fundamental forms determines the projective structure at infinity. As an application, we establish a conjecture of Labourie from 1992 regarding constant Gaussian curvature surfaces. We also derive consequences for constant mean curvature surfaces.
Contact committee chair David Dumas ddumas@uic.edu for zoom meeting password.
Wednesday June 10, 2020 at 1:00 PM in https://uic.zoom.us/j/96653527150