Harmonic forms and norms on cohomology of non-compact hyperbolic 3-manifolds

Abstract: We will talk about generalizations of an inequality of Brock-Dunfield to the non-compact case, with tools from Hodge theory for non-compact hyperbolic manifolds and recent developments in the theory of minimal surfaces. We also prove that their inequality is not sharp, using holomorphic quadratic differentials and recent ideas of Wolf and Wu on minimal geometric foliations. If time permits, we will also describe a partial generalization to the infinite volume case.

Mathematics

Audience: researchers in the discipline

Caltech geometry/topology seminar