Intrinsic perimeter, compactness and Poincar\'e inequality for SBV functions in Carnot-Carath\'eodory spaces

By introducing an intrinsic perimeter measure for intrinsic countably rectifiable sets, we prove a compactness result and a Poincar\'e inequality for special functions with bounded variation in equiregular Carnot-Carath\'eodory spaces which satisfy an additional natural assumption, called property $\mathcal R$.