JournalsrmiVol. 26, No. 3pp. 1035–1056

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

  • Nicolas Juillet

    Université de Grenoble I, Saint-Martin-d'Hères, France
A counterexample for the geometric traveling salesman problem in the Heisenberg group cover
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Abstract

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. 1035–1056

DOI 10.4171/RMI/626