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

DOI10.4171/RMI/626zbMath1206.28003WikidataQ124850534 ScholiaQ124850534MaRDI QIDQ616608

Nicolas Juillet

Publication date: 10 January 2011

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmi/1282913831

zbMATH Keywords

Heisenberg grouptraveling salesman problemrectifiable curveCarnot-Carathéodory metric

Mathematics Subject Classification ID

Length, area, volume, other geometric measure theory (28A75)

Related Items (7)

Riesz transform and vertical oscillation in the Heisenberg group ⋮ Stratified β$\beta$‐numbers and traveling salesman in Carnot groups ⋮ Identifying 1-rectifiable measures in Carnot groups ⋮ Singular integrals on regular curves in the Heisenberg group ⋮ Multiscale analysis of 1-rectifiable measures. II: Characterizations ⋮ The traveling salesman problem in the Heisenberg group: Upper bounding curvature ⋮ An upper bound for the length of a traveling salesman path in the Heisenberg group

Cites Work

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• Menger curvature and Lipschitz parametrizations in metric spaces
• Characterization of Subsets of Rectifiable Curves in R ⁿ
• Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
• Rectifiability and perimeter in the Heisenberg group

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