Lusin approximation and horizontal curves in Carnot groups (Q515359)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Lusin approximation and horizontal curves in Carnot groups |
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Lusin approximation and horizontal curves in Carnot groups |
scientific article |
Statements
Lusin approximation and horizontal curves in Carnot groups (English)
0 references
13 March 2017
0 references
Summary: We show that, given an absolutely continuous horizontal curve \(\gamma\) in the Heisenberg group, there is a \(C^{1}\) horizontal curve \(\Gamma\) such that \(\Gamma =\gamma\) and \(\Gamma^\prime =\gamma^\prime\) outside a set of small measure. Conversely, we construct an absolutely continuous horizontal curve in the Engel group with no \(C^{1}\) horizontal approximation.
0 references
Carnot group
0 references
Heisenberg group
0 references
Engel group
0 references
horizontal curve
0 references
Lusin approximation
0 references
Whitney extension
0 references
