  In this article we extend a euclidean result of David and Semmes to the
Heisenberg group by giving a sufficient condition for a $k$-Ahlfors-regular
subset to have big pieces of bilipschitz images of subsets of $\R^k$. This
Carleson type condition measures how well the set can be approximated by the
Heisenberg $k$-planes at different scales and locations. The proof given here
follow the paper of David and Semmes.
