Whitney’s example by way of Assouad’s embedding

DOI10.1090/S0002-9939-03-06913-2zbMath1061.26010OpenAlexW1938106698MaRDI QIDQ4417247

Piotr Hajłasz

Publication date: 28 July 2003

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

Full work available at URL: https://doi.org/10.1090/s0002-9939-03-06913-2

zbMATH Keywords

critical setvon Koch snowflakeWhitney's extension theoremAssouad embeddingWhitney's example

Mathematics Subject Classification ID

Fractals (28A80) Continuity and differentiation questions (26B05) Special properties of functions of several variables, Hölder conditions, etc. (26B35)

Related Items (10)

Purely 1-unrectifiable metric spaces and locally flat Lipschitz functions ⋮ Toward the theory of Orlicz–Sobolev classes ⋮ Shallow water model for lakes with friction and penetration ⋮ Nonsmooth Morse-Sard theorems ⋮ A nonsmooth Morse--Sard theorem for subanalytic functions ⋮ On the total disconnectedness of the quotient Aubry set ⋮ On the Hausdorff dimension of the mather quotient ⋮ The Morse criticality revisited and some new applications to the Morse-Sard theorem ⋮ Almost bi-Lipschitz embeddings and almost homogeneous sets ⋮ Sard's theorem for mappings in Hölder and Sobolev spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Critical sets in the plane
• Embeddings of Gromov hyperbolic spaces
• Lectures on analysis on metric spaces
• On the nonexistence of bilipschitz parameterizations and geometric problems about \(A_ \infty\)-weights
• Reifenberg flat metric spaces, snowballs, and embeddings
• A function not constant on a connected set of critical points
• A Dense Arcwise Connected Set of Critical Points - Molehills Out of Mountains
• Surjective Mappings Whose Differential is Nowhere Surjective
• A Critical Set with Nonnull Image has Large Hausdorff Dimension
• Plongements lipschitziens dans ${\bbfR}\sp n$
• A quasiconformal group not isomorphic to a Möbius group
• The Degree of Regularity of a Quasiconformal Mapping
• Functions not Constant on Fractal Quasi-Arcs of Critical Points
• Analytic Extensions of Differentiable Functions Defined in Closed Sets
• On the Existence of Functions Having Given Partial Derivatives on a Curve

This page was built for publication: Whitney’s example by way of Assouad’s embedding