A C^m,ω Whitney Extension Theorem for Horizontal Curves in the Heisenberg Group

2022/04/07 by Gareth Speight, Speight, Gareth, Scott Zimmerman +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2204.03544

openalex publication_date 2022/04/07 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

We characterize which mappings from a compact subset of ℝ into the Heisenberg group can be extended to a C^m,ω horizontal curve for a given modulus of continuity ω. We motivate our characterization by showing that the C^m,ω extension property fails if we instead use a more direct analogue of the conditions from the C^m case.

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