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

• DOI: 10.4171/rmi/889
• Publication Date: 2016-06-08T21:45:12Z
• Authors: Sean Li; Raanan Schul
• Keywords: Heisenberg group; Path length

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