Lusin approximation and horizontal curves in Carnot groups

• Gareth Speight ^[1]
  1. [1] University of Cincinnati

     University of Cincinnati

     City of Cincinnati, Estados Unidos

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 32, Nº 4, 2016, págs. 1423-1444
• Idioma: inglés
• DOI: 10.4171/RMI/924
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.