Seminario di analisi matematica
ore
16:00
presso Aula Vitali
The talk will be concerned with s-minimal surfaces, that is,
hypersurfaces of R^n with zero nonlocal mean curvature. These are the
equations associated to critical points of the fractional s-perimeter.
We will present a recent result in collaboration with M. Cozzi in which
we establish, in any dimension, a gradient estimate for nonlocal minimal
graphs. It leads to their smoothness, a result that was only known for
n=2 and 3 (but without a quantitative bound); in higher dimensions only
their continuity had been established. We will also present a work with
E. Cinti and J. Serra in which we prove that half spaces are the only
stable s-minimal cones in R^3 for s sufficiently close to 1.