Mathematics

We discuss the notion of nonlocal minimal surfaces  (that are hypersurfaces that minimize a nonlocal perimeter functional) and nonlocal minimal cones (that are homogeneous nonlocal minimal surfaces). We prove that the only nonlocal minimal cones in the plane are the hyperplanes. This implies that nonlocal minimal surfaces are in the plane are locally smooth curves. These results were obtained in a joint work with O. Savin.