The traveling salesman problem in the Heisenberg group: Upper bounding curvature

DOI10.1090/tran/6501zbMath1350.53044arXiv1307.0050OpenAlexW2963427092MaRDI QIDQ2790632

Sean Li, Raanan Schul

Publication date: 7 March 2016

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.0050

zbMATH Keywords

Heisenberg groupcurvaturetraveling salesman theoremJones \(\beta\) numbers

Mathematics Subject Classification ID

Length, area, volume, other geometric measure theory (28A75) Sub-Riemannian geometry (53C17)

Related Items (21)

The strong geometric lemma for intrinsic Lipschitz graphs in Heisenberg groups ⋮ Nonnegative kernels and 1-rectifiability in the Heisenberg group ⋮ Generalized rectifiability of measures and the identification problem ⋮ The traveling salesman theorem in Carnot groups ⋮ The traveling salesman theorem for Jordan curves ⋮ Hölder curves and parameterizations in the Analyst's traveling salesman theorem ⋮ Riesz transform and vertical oscillation in the Heisenberg group ⋮ Composing and decomposing surfaces and functions ⋮ Stratified β$\beta$‐numbers and traveling salesman in Carnot groups ⋮ Globally well-posedness results of the fractional Navier-Stokes equations on the Heisenberg group ⋮ A \(d\)-dimensional analyst's travelling salesman theorem for subsets of Hilbert space ⋮ Identifying 1-rectifiable measures in Carnot groups ⋮ An existence and uniqueness result for the Navier-Stokes type equations on the Heisenberg group ⋮ Quantitative comparisons of multiscale geometric properties ⋮ Singular integrals on regular curves in the Heisenberg group ⋮ Markov convexity and nonembeddability of the Heisenberg group ⋮ Multiscale analysis of 1-rectifiable measures. II: Characterizations ⋮ A sharp necessary condition for rectifiable curves in metric spaces ⋮ An upper bound for the length of a traveling salesman path in the Heisenberg group ⋮ Effective Reifenberg theorems in Hilbert and Banach spaces ⋮ The restricted content and the \(d\)-dimensional Analyst's travelling salesman theorem for general sets

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• Coarse differentiation and quantitative nonembeddability for Carnot groups
• The geometric traveling salesman problem in the Heisenberg group
• Subadditivity of Homogeneous Norms on Certain Nilpotent Lie Groups
• Menger curvature and Lipschitz parametrizations in metric spaces
• Characterization of Subsets of Rectifiable Curves in R ⁿ
• A T(b) theorem with remarks on analytic capacity and the Cauchy integral

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