A $C^m$ Whitney Extension Theorem for Horizontal Curves in Free Step $2$ Carnot Groups

Hyogo Shibahara

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arXiv · 2308.01991

A $C^m$ Whitney Extension Theorem for Horizontal Curves in Free Step $2$ Carnot Groups

Hyogo Shibahara

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Abstract

We establish a $C^m$ Whitney extension theorem for horizontal curves in free step~$2$ Carnot groups $\mathbb{G}_r$ for an arbitrary number of generators $r \geq 2$. This extends existing results in the Heisenberg group. New techniques include a quantitative linear dependence structure on jets on the horizontal layer, a discretization process to correct vertical areas, and studying the effect of unrelated vertical areas.

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Hyogo Shibahara. 2023-08-03. A $C^m$ Whitney Extension Theorem for Horizontal Curves in Free Step $2$ Carnot Groups. https://arxiv.org/abs/2308.01991

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