Sobolev mappings and the Rumin complex
Differential Geometry
2021-01-13 v1
Abstract
We consider contact manifolds equipped with Carnot-Caratheodory metrics, and show that the Rumin complex is respected by Sobolev mappings: Pansu pullback induces a chain mapping between the smooth Rumin complex and the distributional Rumin complex. As a consequence, the Rumin flat complex -- the analog of the Whitney flat complex in the setting of contact manifolds -- is bilipschitz invariant. We also show that for Sobolev mappings between general Carnot groups, Pansu pullback induces a chain mapping when restricted to a certain differential ideal of the de Rham complex. Both results are applications of the Pullback Theorem from our previous paper.
Cite
@article{arxiv.2101.04528,
title = {Sobolev mappings and the Rumin complex},
author = {Bruce Kleiner and Stefan Muller and Xiangdong Xie},
journal= {arXiv preprint arXiv:2101.04528},
year = {2021}
}