Abstract:
Submanifolds with intrinsic Lipschitz regularity in sub-Riemannian Heisenberg groups can be introduced using the theory of intrinsic Lipschitz graphs started by B. Franchi, R. Serapioni and F. Serra Cassano almost 15 years ago. The main related question concerns a Rademacher-type theorem (i.e., existence of "tangent" plane) for such graphs: in this talk we discuss a recent positive solution to the problem. The proof uses the language of currents in Heisenberg groups and, in particular, (a version of) the celebrated Constancy Theorem. A number of complementary results (e.g., extension and smooth approximation theorems for intrinsic Lipschitz graphs) is also utilized. Time permitting, some applications of the Rademacher theorem (e.g., an area formula and a Lusin-type theorem) will be discussed. The talk will be kept at an introductory level.
