Higher order Whitney extension and Lusin approximation for Horizontal curves in the Heisenberg group

2023/10/10 by Andrea Pinamonti, Pinamonti, Andrea, Gareth Speight +3
Computer Science · Mathematics · #53C17 #58C25 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2310.06953

openalex publication_date 2023/10/10 · openalex created_date 2023/10/13 · openalex updated_date 2026/07/28

Abstract

In the setting of horizontal curves in the Heisenberg group, we prove a C^m,ω finiteness principle, a C^m,ω Lusin approximation result, a C^∞ Whitney extension result, and a C^∞ Lusin approximation result. Combined with previous work, this completes the study of Whitney extension and Lusin approximation for horizontal curves of class C^m, C^m,ω, and C^∞ in the Heisenberg group.

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