The Whitney Extension Theorem for C¹, horizontal curves in the Heisenberg group

2015/07/08 by Zimmerman, Scott · 1 citation
#53C17 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1507.02240

Abstract

For a real valued function defined on a compact set K ⊂ ℝ^m, the classical Whitney Extension Theorem from 1934 gives necessary and sufficient conditions for the existence of a C^k extension to ℝ^m. In this paper, we prove a version of the Whitney Extension Theorem in the case of C¹, horizontal extensions for mappings defined on compact subsets of ℝ taking values in the Heisenberg Group ℍⁿ.

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• Directional Pliability, Whitney Extension, and Lusin Approximation for Curves in Carnot Groups

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