Variational Methods in Geomatry

The problem of finding metrics with constant Q-curvature in a prescribed conformal class is an important fourth-order cousin of the Yamabe problem. In this talk, I will explain how certain variational bifurcation techniques used to prove non...

A Riemannian manifold is called Besse, if all of its geodesics are periodic. The goal of this talk is to study the energy functional on the free loop space of a Besse manifold. In particular, we show that this is a perfect Morse-Bott function for...

In the 80s Pitts-Rubinstein conjectured that certain kinds of Heegaard surfaces in three-manifolds can be isotoped to index 1 minimal surfaces. I'll describe in detail a proof of their conjecture and some applications. This is joint work with...

We consider the classical problem of prescribing the scalar curvature of a manifold via conformal deformation of the metric, dating back to works by Kazdan and Warner. This problem is mainly understood in low dimensions, where blow-ups of solutions...