  We obtain a blow-up theorem for regular submanifolds in the Heisenberg group,
where intrinsic dilations are used. Main consequence of this result is an
explicit formula for the density of (p+1)-dimensional spherical Hausdorff
measure restricted to a p-dimensional submanifold with respect to the
Riemannian surface measure. We explicitly compute this formula in some simple
examples and we present a lower semicontinuity result for the spherical
Hausdorff measure with respect to the weak convergence of currents. Another
application is the proof of an intrinsic coarea formula for vector-valued
mappings on the Heisenberg group.
