Revista Matemática Iberoamericana


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Volume 26, Issue 3, 2010, pp. 1035–1056
DOI: 10.4171/RMI/626

Published online: 2010-12-31

A counterexample for the geometric traveling salesman problem in the Heisenberg group

Nicolas Juillet[1]

(1) Université de Grenoble I, Saint-Martin-d'Hères, France

We are interested in characterizing the compact sets of the Heisenberg group that are contained in a curve of finite length. Ferrari, Franchi and Pajot recently gave a sufficient condition for those sets, adapting a necessary and sufficient condition due to P. Jones in the Euclidean setting. We prove that this condition is not necessary.

Keywords: Heisenberg group, Carnot-Carathéodory metric, rectifiable curve, Traveling Salesman Problem

Juillet Nicolas: A counterexample for the geometric traveling salesman problem in the Heisenberg group. Rev. Mat. Iberoam. 26 (2010), 1035-1056. doi: 10.4171/RMI/626