Mathematics

The Willmore functional of an immersed surface in a Riemannian manifold is the L2 norm of the mean curvature. The functional appears in many fields of mathematics and science in general: in biology (Helfrich energy), in general relativity (Hawking mass), optics, etc. After an introduction to the topic, in the seminar I will present a joint work with A. Malchiodi and N. Ikoma where we construct Willmore tori in Riemannian manifolds. The construction is based on a Lyapunov-Schmidt reduction, a very versatile perturbative technique in nonlinear analysis. In particular I will discuss the case the ambient manifold is the Schwarzschild space, one of the most studied manifolds in general relativity.