Lusin Approximation and Horizontal Curves in Carnot Groups

2014/12/08 by Gareth Speight, Speight, Gareth · 1 citation
Mathematics · #43A80 #46E35 #49J52 #49Q15 #53C17 #FOS: Mathematics #Metric Geometry (math.MG) #math.MG #msc:43A80 #msc:46E35 #msc:49J52 #msc:49Q15 #msc:53C17

paper · pdf · doi:10.48550/arxiv.1412.2531

21 pages. Corrected a technical error in the argument for the Heisenberg group and added previously omitted proofs. Improved the exposition and corrected typos as suggested by referees. To appear in Revista Matematica Iberoamericana

arxiv created 2015/11/25 · arxiv updated 2015/11/26

Abstract

We show that, given an absolutely continuous horizontal curve γ in the Heisenberg group, there is a C¹ horizontal curve Γ such that Γ=γ and Γ'=γ' outside a set of small measure. Conversely, we construct an absolutely continuous horizontal curve in the Engel group with no C¹ horizontal approximation.

Cited by

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

Related

• Lusin approximation for horizontal curves in step 2 Carnot groups
• Higher order Whitney extension and Lusin approximation for Horizontal curves in the Heisenberg group
• Directional Pliability, Whitney Extension, and Lusin Approximation for Curves in Carnot Groups
• A C^m Whitney Extension Theorem for Horizontal Curves in Free Step 2 Carnot Groups
• A C^m,ω Whitney Extension Theorem for Horizontal Curves in the Heisenberg Group