# 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.

#### 4 Citations

GAMMA-CONVERGENCE OF GAUSSIAN FRACTIONAL PERIMETER

- 2021

We prove the Γ-convergence of the renormalised Gaussian fractional s-perimeter to the Gaussian perimeter as s → 1−. Our definition of fractional perimeter comes from that of the fractional powers of… Expand

A quantitative dimension free isoperimetric inequality for the fractional Gaussian perimeter

- Mathematics
- 2020

The Gaussian isoperimetric inequality states that among all sets with prescribed Gaussian measure, the halfspace is the one with least Gaussian perimeter. This result has been proved independently by… Expand

Gamma-convergence of fractional Gaussian perimeter

- Mathematics
- 2021

We prove the Γ-convergence of the renormalised fractional Gaussian s-perimeter to the Gaussian perimeter as s → 1−. Our definition of fractional perimeter comes from that of the fractional powers of… Expand

A quantitative dimension free isoperimetric inequality for the Gaussian fractional perimeter

- Mathematics
- 2020

We prove a quantitative isoperimetric inequality for the Gaussian fractional perimeter using extension techniques. Though the exponent of the Fraenkel asymmetry is not sharp, the constant appearing… Expand

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