Inserted: 5 apr 2020
Last Updated: 1 jun 2020
We prove the local minimality of halfspaces in Carnot groups for a class of nonlocal functionals usually addressed as nonlocal perimeters. Moreover, in a class of Carnot groups in which the De Giorgi's rectifiability Theorem holds, we provide a lower bound for the $\Gamma$-liminf of the rescaled energy in terms of the horizontal perimeter.
Keywords: Carnot groups, Sets of finite perimeter, Rectifiability, $\Gamma$-convergence, calibrations, nonlocal perimeters