We show a quantitative version of the isoperimetric inequality for a non local perimeter of Minkowski type. We also apply this result to study isoperimetric problems with repulsive interaction terms, under volume and convexity constraints.We prove existence of minimizers, and we describe their shape as the volume tends to zero or to infinity.
@article{bwmeta1.element.doi-10_1515_geofl-2017-0003,
author = {Annalisa Cesaroni and Matteo Novaga},
title = {Isoperimetric problems for a nonlocal perimeter of Minkowski type},
journal = {Geometric Flows},
volume = {2},
year = {2017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_geofl-2017-0003}
}
Annalisa Cesaroni; Matteo Novaga. Isoperimetric problems for a nonlocal perimeter of Minkowski type. Geometric Flows, Tome 2 (2017) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_geofl-2017-0003/