Two characterization of BV functions on Carnot groups via the heat semigroup (Q2917603)

In the very interesting paper under review, the authors provide two different characterizations of sets with finite perimeter and functions of bounded variation in a Carnot groups, analogous to those in the Euclidean settings, 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.