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August, 2007 The Geometric Traveling Salesman Problem in the Heisenberg Group
Fausto Ferrari, Bruno Franchi , Hervé Pajot
Rev. Mat. Iberoamericana 23(2): 437-480 (August, 2007).


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


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Fausto Ferrari. Bruno Franchi . Hervé Pajot. "The Geometric Traveling Salesman Problem in the Heisenberg Group." Rev. Mat. Iberoamericana 23 (2) 437 - 480, August, 2007.


Published: August, 2007
First available in Project Euclid: 26 September 2007

zbMATH: 1142.28004
MathSciNet: MR2371434

Primary: 28A75

Keywords: Carnot-Carathéodory metric , Heisenberg group , rectifiable curve , Traveling salesman problem

Rights: Copyright © 2007 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.23 • No. 2 • August, 2007
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