Isoperimetric sets on Carnot groups

We prove the existence of isoperimetric sets in any Carnot group,that is, sets minimizing the intrinsic perimeter among all measurable setswith prescribed Lebesgue measure. We also show that, up to a null set,these isoperimetric sets are open, bounded, their boundary is Ahlfors-regularand they satisfy the condition B. Furthermore, in the particular case of theHeisenberg group, we prove that any reduced isoperimetric set is a domain ofisoperimetry. All these properties are satisfied with implicit constants thatdepend only on the dimension of the group and on the prescribed Lebesguemeasure.