Hölder continuous mappings, differential forms and the Heisenberg groups

Abstract

We develop analysis of Hölder continuous mappings with applications to geometry and topology of the Heisenberg groups. We cover the theory of distributional Jacobians of Hölder continuous mappings and pullbacks of differential forms under Hölder continuous mappings. That includes versions of the change of variables formula and the Stokes theorem for Hölder 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 Hölder homotopy groups of the Heisenberg groups.