An upper bound for the length of a traveling salesman path in the Heisenberg group

• Sean Li ^[1] ; Raanan Schul ^[2]
  1. [1] University of Chicago

     University of Chicago

     City of Chicago, Estados Unidos

     
  2. [2] Stony Brook University

     Stony Brook University

     Town of Brookhaven, Estados Unidos

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 32, Nº 2, 2016, págs. 391-417
• Idioma: inglés
• DOI: 10.4171/RMI/889
• Texto completo no disponible (Saber más ...)
• Resumen

  • We show that a sufficient condition for a subset E in the Heisenberg group (endowed with the Carnot–Carathéodory metric) to be contained in a rectifiable curve is that it satisfies a modified analogue of Peter Jones’s geometric lemma. Our estimates improve on those of [6], allowing for any power r < 4 to replace the power 2 of the Jones-β-number. This complements in an open ended way our work in [13], where we showed that such an estimate was necessary, however with the power r = 4.