Two Characterization of BV Functions on Carnot Groups via the Heat Semigroup

In this paper we provide two different characterizations of sets with finite perimeter and functions of bounded variation in Carnot groups, analogous to those that hold in Euclidean spaces, in terms of the short-time behavior of the heat semigroup. The second one holds under the hypothesis that the reduced boundary of a set of finite perimeter is rectifiable, a result that presently is known in Step 2 Carnot groups.