Local minimizers and gamma-convergence for nonlocal perimeters in Carnot groups

@article{Carbotti2020LocalMA,
  title={Local minimizers and gamma-convergence for nonlocal perimeters in Carnot groups},
  author={Alessandro Carbotti and Sebastiano Don and Diego Pallara and Andrea Pinamonti},
  journal={arXiv: Analysis of PDEs},
  year={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. 
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