Hölder curves and parameterizations in the Analyst's traveling salesman theorem

DOI10.1016/j.aim.2019.04.011zbMath1411.28001arXiv1806.01197OpenAlexW2962804025MaRDI QIDQ2419274

Lisa Naples, Matthew Badger, Vyron Vellis

Publication date: 29 May 2019

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.01197

zbMATH Keywords

parameterizationJones' beta numbersfractional rectifiabilityHölder curvesAnalyst's traveling salesman problemtube approximations

Mathematics Subject Classification ID

Numerical smoothing, curve fitting (65D10) Lipschitz (Hölder) classes (26A16) Length, area, volume, other geometric measure theory (28A75) Fractals (28A80) Geometric embeddings of metric spaces (30L05)

Related Items (14)

Fractal percolation is unrectifiable ⋮ Generalized rectifiability of measures and the identification problem ⋮ Box-counting by Hölder's traveling salesman ⋮ The traveling salesman theorem for Jordan curves ⋮ Subsets of rectifiable curves in Banach spaces. I: Sharp exponents in traveling salesman theorems ⋮ Subsets of rectifiable curves in Banach spaces. II: Universal estimates for almost flat arcs ⋮ Stratified β$\beta$‐numbers and traveling salesman in Carnot groups ⋮ A \(d\)-dimensional analyst's travelling salesman theorem for subsets of Hilbert space ⋮ Identifying 1-rectifiable measures in Carnot groups ⋮ Time complexity of the analyst's traveling salesman algorithm ⋮ Sufficient conditions for C^1,α parametrization and rectifiability ⋮ Hölder parameterization of iterated function systems and a self-affine phenomenon ⋮ The restricted content and the \(d\)-dimensional Analyst's travelling salesman theorem for general sets ⋮ Radon measures and Lipschitz graphs

Uses Software

• Concorde

Cites Work

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