Pansu pullback and rigidity of mappings between Carnot groups

TL;DR

This paper develops new structural results for Sobolev and quasisymmetric mappings between Carnot groups, establishing partial rigidity and regularity theorems in the context of geometric mapping theory on equiregular manifolds.

Contribution

It introduces novel rigidity and regularity results for mappings in Carnot groups, expanding understanding of geometric mapping theory in these structures.

Findings

Partial rigidity theorems for Sobolev mappings

New regularity results for quasisymmetric maps

Structural insights into mappings on equiregular manifolds

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.