Higher dimensional Ahlfors regular sets and chordarc curves in \(R^n\)

DOI10.1216/rmjm/1181071829zbMath0932.28004OpenAlexW2090456021MaRDI QIDQ1288319

David A. Herron, Manouchehr Ghamsari

Publication date: 16 February 2000

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://math.la.asu.edu/~rmmc/rmj/Vol28-1/CONT281/CONT281.html

zbMATH Keywords

Hausdorff dimensionHausdorff measurerectifiable curvevon Koch snowflakeJordan curveboundary turning

Mathematics Subject Classification ID

Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Length, area, volume, other geometric measure theory (28A75) Fractals (28A80) Hausdorff and packing measures (28A78)

Related Items (10)

Möbius bilipschitz homogeneous arcs on the plane ⋮ Inversion invariant bilipschitz homogeneity ⋮ Bilipschitz homogeneity and inner diameter distance ⋮ Iterated function system quasiarcs ⋮ Bilipschitz homogeneous Jordan curves, Möbius maps, and dimension ⋮ Bi-Lipschitz homogeneous curves in ℝ² are quasicircles ⋮ The fractal ``frog ⋮ Fractal inner chordarc disks ⋮ Toward a quasi-Möbius characterization of invertible homogeneous metric spaces ⋮ Bilipschitz homogeneous Jordan curves

Cites Work

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• Bilipschitz extensions of maps having quasiconformal extensions
• Harmonic measure and arclength
• Digital sundials, paradoxical sets, and Vitushkin's conjecture
• Opérateurs intégraux singuliers sur certaines courbes du plan complexe
• Extension of quasisymmetric and Lipschitz embeddings of the real line into the plane
• Classification of a quasi-circles by Hausdorff dimension
• Hardy spaces, $A_\infty$, and singular integrals on chord-arc domains

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