Isoperimetric problems for a nonlocal perimeter of Minkowski type (Q1698603)

The authors prove a quantitative version of the isoperimetric inequality for a non local perimeter of Minkowski type, based on recent results on a quantitative Brunn-Minkowski inequality. Isoperimetric problems are studied in presence of nonlocal repulsive interaction terms under convexity constraints. Existence of minimizers for every volume is shown. In particular, balls are shown to be minimizers for small volumes. A description of the asymptotic shape of minimizers in the large volume regime is provided.