Geometry and Topology Seminar: "Norm of Cohomology and Minimal Surfaces in Hyperbolic 3-manifolds"
Speaker: Xiaolong Han, UIUC
Abstract: In this talk, we will talk about generalization of an inequality of Brock-Dunfield to the non-compact case, with tools from Hodge theory for the non-compact hyperbolic manifolds and recent development of minimal surfaces. We will also prove that their inequality is not sharp, using the property of holomorphic quadratic differential or recent ideas of geometric foliation of Wolf and Wu. Time dependent, we will introduce two functionals which unify various results and ask interesting new questions.
Host: Yanli Song