Sets with finite $${\mathbb H}$$ -perimeter and controlled normal

Abstract

In the Heisenberg group, we prove that the boundary of sets with finite \({\mathbb H}\)-perimeter and having a bound on the measure theoretic normal is an \({\mathbb H}\)-Lipschitz graph. Then we show that if the normal is, on the boundary, the restriction of a continuous mapping, then the boundary is an \({\mathbb H}\)-regular surface.