In their pioneering work, Korevaar and Schoen defined the Sobolev spaces of functions with target in a metric space. Among many results, they were able to obtain satisfactory existence and regularity results for energy minimizers under the assumptions that the Alexandrov curvature of the target space is non-positive. Some years later Capogna and Lin proved similar results in the Heisenberg group H^n, a metric space with unbounded Alexandrov curvature. They were able to obtain the existence for energy minimizers for any n and regularity for n=2. In this talk I will retrace the work of Capogna and Lin and I will explain how, together with Adamowicz and Warhurst, we are studying the extention of the regularity result to any n.

Meeting ID: 880 9117 0519 Passcode: 005694