Lipschitz non-extension theorems into jet space Carnot groups

TL;DR

This paper establishes non-extension theorems for Lipschitz maps into jet space Carnot groups, including Heisenberg groups, highlighting limitations of Lipschitz extensions in these geometric contexts.

Contribution

It introduces new non-extendability results for Lipschitz maps into jet spaces with Riemannian and sub-Riemannian distances, advancing understanding of Lipschitz geometry in Carnot groups.

Findings

Lipschitz maps cannot be extended into certain jet spaces.

Results apply to all Heisenberg groups.

Highlights geometric constraints in Lipschitz extension problems.

Abstract

We prove non-extendability results for Lipschitz maps with target space being jet spaces equipped with a left-invariant Riemannian distance, as well as jet spaces equipped with a left-invariant sub-Riemannian Carnot-Caratheodory distance. The jet spaces give a model for a certain class of Carnot groups, including in particular all Heisenberg groups.