A nonlocal Willmore Energy

I will discuss a natural definition of a nonlocal version of the Willmore
energy -- based on Caffarelli-Roquejoffre-Savin's mean curvature notion -- and
their relation to the so-called tangent-point energies, with consequences for
existence of minimizers in subcritical and critical regimes.

Based on joint works with S. Blatt, G. Giacomin, J. Scheuer.