Rigidity of quasiconformal maps on Carnot groups

TL;DR

This paper proves that quasiconformal maps on certain Carnot groups are necessarily biLipschitz, revealing rigidity properties that impact the understanding of quasiisometries between negatively curved solvable Lie groups.

Contribution

It establishes biLipschitz rigidity of quasiconformal maps on 2-step Carnot groups with reducible first layer, a significant advancement in geometric analysis.

Findings

Quasiconformal maps on many Carnot groups are biLipschitz.

Results apply specifically to 2-step Carnot groups with reducible first layer.

Implications for rigidity of quasiisometries between negatively curved solvable Lie groups.

Abstract

We show that quasiconformal maps on many Carnot groups must be biLipschitz. In particular, this is the case for 2-step Carnot groups with reducible first layer. These results have implications for the rigidity of quasiisometries between negatively curved solvable Lie groups.