A note on pliability and the openness of the multiexponential map in Carnot groups

TL;DR

This paper compares different notions of non-rigidity of horizontal vectors in Carnot groups, motivated by their roles in monotone set characterization and Whitney extension properties.

Contribution

It provides a comparative analysis of various concepts of non-rigidity in Carnot groups, clarifying their relationships and implications.

Findings

Different notions of non-rigidity are compared and contrasted.

The relationships between these notions are clarified.

Implications for monotone sets and Whitney extension are discussed.

Abstract

In recent years, several notions of non-rigidity of horizontal vectors in Carnot groups have been proposed, motivated, in particular, by the characterization of monotone sets and Whitney extension properties. In this note we compare some of these notions.