# Analysis Seminar

#### Nonlocal minimal cones and surfaces with constant nonlocal mean curvature

Speaker: Xavier Cabre, ICREA and UPC, Barcelona

Location: Warren Weaver Hall 1302

Date: Thursday, December 14, 2017, 11 a.m.

Synopsis:

The talk will be concerned with hypersurfaces of R^n with zero, or constant, nonlocal mean curvature. These are the equations associated to critical points of the fractional s-perimeter. We prove that half spaces are the only stable s-minimal cones in R^3 for s sufficiently close to 1. We will then turn to the nonlocal analogue of the Alexandrov result characterizing spheres as the only closed embedded hypersurfaces in R^n with constant mean curvature. Finally, we will describe results establishing the existence of periodic Delaunay-type cylinders in R^n, as well as periodic lattices made of near-spheres, with constant nonlocal mean curvature.