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.
Cite this article
Nicolas Juillet, A counterexample for the geometric traveling salesman problem in the Heisenberg group. Rev. Mat. Iberoam. 26 (2010), no. 3, pp. 1035–1056DOI 10.4171/RMI/626