Calculus of Variations and Geometric Measure Theory
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A. Pinamonti - G. Speight - S. Zimmerman

A $C^m$ Whitney extension theorem for horizontal curves in the Heisenberg group

created by pinamonti on 20 Jul 2018
modified on 13 Jan 2019


Accepted Paper

Inserted: 20 jul 2018
Last Updated: 13 jan 2019

Journal: Trans AMS
Year: 2018


We characterize those mappings from a compact subset of $\mathbb{R}$ into the Heisenberg group $\mathbb{H}^n$ which can be extended to a $C^m$ horizontal curve in $\mathbb{H}^n$. The characterization combines the classical Whitney conditions with an estimate comparing changes in the vertical coordinate with those predicted by the Taylor series of the horizontal coordinates.


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