Compensated compactness, div--curl theorem and $H$-convergence in general Heisenberg groups

In this paper we present some recent results concerning existence and estimates of the fundamental solution for hypoelliptic differential operators in the contact complex of Heisenberg groups, and their application to the compensated compactess for intrinc Heisenberg differential forms. As a consequence, we prove a general div--rot theorem for horizontal vector fields and a compactness theorem with respect to the $H$--convergence of differential operators in general Heisenberg groups $he n$ with $nge 1$.