Pansu pullback and rigidity of mappings between Carnot groups
Differential Geometry
2021-12-21 v2 Metric Geometry
Abstract
This is the first in a series of papers on geometric mapping theory in Carnot groups -- and more generally equiregular manifolds -- in which we prove a number of new structural results for Sobolev (in particular quasisymmetric) mappings, establishing (partial) rigidity or (partial) regularity theorems, depending on the context.
Keywords
Cite
@article{arxiv.2004.09271,
title = {Pansu pullback and rigidity of mappings between Carnot groups},
author = {Bruce Kleiner and Stefan Muller and Xiangdong Xie},
journal= {arXiv preprint arXiv:2004.09271},
year = {2021}
}
Comments
Original version was split into two parts; the first part appears here, and the second part is arXiv:2112.01866. Added treatment of equiregular manifolds (Appendix A). Simplified treatment of center of mass. Moved result on the differential ideal J to arXiv:2101.04528. References updated; many small corrections made