Monotone sets and local minimizers for the perimeter in Carnot groups

Monotone sets have been introduced about ten years ago by Cheeger and Kleiner who reduced the proof of non biLipschitz embeddability Heisenberg group into L1 to classification its monotone subsets. Later on, played an important role in several works related geometric measure theory issues setting. In this paper, we work arbitrary Carnot show that subsets are with locally finite perimeter local minimizers for perimeter. Under additional condition on ambient group, prove their measure-theoretic interior support precisely monotone. We also topological properties whose interest is independent from study sets. As a combination our results, get particular sufficient under which any set admits representatives