Calculus of Variations and Geometric Measure Theory

A. Carbotti - S. Don - D. Pallara - A. Pinamonti

Local minimizers and Gamma-convergence for nonlocal perimeters in Carnot Groups

created by carbotti on 05 Apr 2020
modified on 17 Mar 2021


Published Paper

Inserted: 5 apr 2020
Last Updated: 17 mar 2021

Journal: ESAIM cocv
Pages: 30
Year: 2021

ArXiv: 2004.02314 PDF


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.

Tags: GeoMeG
Keywords: Carnot groups, Sets of finite perimeter, Rectifiability, $\Gamma$-convergence, calibrations, nonlocal perimeters