Hölder continuous mappings, differential forms and the Heisenberg groups

Abstract: We develop analysis of H\"older continuous mappings with applications to geometry and topology of the Heisenberg groups. We cover the theory of distributional Jacobians of H\"older continuous mappings and pullbacks of differential forms under H\"older continuous mappings. That includes versions of the change of variables formula and the Stokes theorem for H\"older continuous mappings. The main applications are in the setting of the Heisenberg groups, where we provide a simple proof of a generalization of the Gromov non-embedding theorem, and new results about the H\"older homotopy groups of the Heisenberg groups.