Abstract: Recently, in a joint work with Bruno Franchi and Pierre Pansu, we have proved some new interior Poincaré and Sobolev inequalities for the Rumin complex in the Heisenberg group in the endpoint situation p = Q (the homogeneous group dimension) or p = Q/2, depending on the degree of the forms. We refer to these inequalities as (\infty, Q)-Poincaré or Sobolev inequalities (or (\infty, Q/2)-Poincaré or Sobolev inequalities respectively). These results complement and complete the program on Poincaré-Sobolev inequalities that we developed in a series of previous papers for $1\le p< Q$ (or p<Q/2). In this talk I'll present a further improvement of the global (\infty, Q)-Poincaré inequality, still obtained in collaboration with Franchi and Pansu, showing that it possible to upgrade bounded primitives to bounded and continuous primitives in the case (\infty, Q) (or (\infty, Q/2), depending on the degree of the forms). The argument we use relies on our previous results and duality (i.e. Hahn-Banach) and generalizes to differential forms a Bourgain-Brezis's duality argument for a Poincaré inequality for periodic functions (Bourgain-Brezis, JAMS 2003).