JournalsrmiVol. 23, No. 2pp. 437–480

The Geometric Traveling Salesman Problem in the Heisenberg Group

  • Fausto Ferrari

    Università di Bologna, Italy
  • Bruno Franchi

    Università di Bologna, Italy
  • Hervé Pajot

    Université Grenoble I, Saint-Martin-d'Hères, France
The Geometric Traveling Salesman Problem in the Heisenberg Group cover
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Abstract

In the Heisenberg group H{\mathbb H} (endowed with its Carnot-Carathéodory structure), we prove that a compact set EHE \subset {\mathbb H} which satisfies an analog of Peter Jones' geometric lemma is contained in a rectifiable curve. This quantitative condition is given in terms of Heisenberg β\beta numbers which measure how well the set EE is approximated by Heisenberg straight lines.

Cite this article

Fausto Ferrari, Bruno Franchi, Hervé Pajot, The Geometric Traveling Salesman Problem in the Heisenberg Group. Rev. Mat. Iberoam. 23 (2007), no. 2, pp. 437–480

DOI 10.4171/RMI/502