Functions not Constant on Fractal Quasi-Arcs of Critical Points

DOI10.2307/2048819zbMath0682.28006OpenAlexW4230560126MaRDI QIDQ4731409

Alec Norton

Publication date: 1989

Full work available at URL: https://doi.org/10.2307/2048819

zbMATH Keywords

Hausdorff dimensionHausdorff measurecritical arccriticality properties of quasi-arcsfractal quasi-arcsMorse-Sard-type theorems

Mathematics Subject Classification ID

Length, area, volume, other geometric measure theory (28A75) Continuity and differentiation questions (26B05) Geometric function theory (30C99) Differentiable maps on manifolds (58C25)

Related Items (16)

Conformal irregularity for Denjoy diffeomorphisms of the 2-torus ⋮ The Zygmund Morse-Sard theorem ⋮ A Sard theorem for tame set-valued mappings ⋮ Purely 1-unrectifiable metric spaces and locally flat Lipschitz functions ⋮ The geometry of Whitney's critical sets ⋮ On strict Whitney arcs and \(t\)-quasi self-similar arcs ⋮ Constructing Whitney sets via IFS with condensation ⋮ On invariant sets in Lagrangian graphs ⋮ Constant distance boundaries of the \(t\)-quasicircle and the Koch snowflake curve ⋮ Relations among Whitney sets, self-similar arcs and quasi-arcs ⋮ The Gauss-Green theorem for fractal boundaries ⋮ On the image size of singular maps. II ⋮ Nonsmooth Morse-Sard theorems ⋮ Numerical Integration of Vector Fields Over Curves with Zero Area ⋮ Whitney’s example by way of Assouad’s embedding ⋮ Some remarks about the Morse-Sard theorem and approximate differentiability

Cites Work

• Étude de quelques algèbres tayloriennes
• Whitney sets and sets of constancy. On a problem of Whitney
• On Jordan arcs and Lipschitz classes of functions defined on them
• A function not constant on a connected set of critical points
• A Critical Set with Nonnull Image has Large Hausdorff Dimension
• Analytic Extensions of Differentiable Functions Defined in Closed Sets
• The measure of the critical values of differentiable maps
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