The Zygmund Morse-Sard theorem

DOI10.1007/BF02921589zbMath0802.58010MaRDI QIDQ1336082

Alec Norton

Publication date: 19 December 1994

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

zbMATH Keywords

Lipschitz spacemodulus of continuitycritical valuesMorse-Sard theoremmeasure zero

Mathematics Subject Classification ID

Continuity and differentiation questions (26B05) Special properties of functions of several variables, Hölder conditions, etc. (26B35) Theory of singularities and catastrophe theory (58K99) Differentiable maps on manifolds (58C25)

Related Items (10)

Sard theorems for Lipschitz functions and applications in optimization ⋮ On sets of critical values in the real line ⋮ The generalized Morse-Sard theorem ⋮ On invariant sets in Lagrangian graphs ⋮ The Morse-Sard theorem for Sobolev spaces in a borderline case ⋮ Nonsmooth Morse-Sard theorems ⋮ A general version of the Morse-Sard theorem ⋮ Selections of bounded variation for roots of smooth polynomials ⋮ Unnamed Item ⋮ Hölder-Zygmund classes on smooth curves

Cites Work

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• Lipschitz spaces, smoothness of functions, and approximation theory
• On the image size of singular maps. II
• A function not constant on a connected set of critical points
• A Critical Set with Nonnull Image has Large Hausdorff Dimension
• Toward a Precise Smoothness Hypothesis in Sard's Theorem
• Functions not Constant on Fractal Quasi-Arcs of Critical Points
• On Differentiable Transformations in R n
• The measure of the critical values of differentiable maps

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