A sufficient condition for the \(C^H\)-rectifiability of Lipschitz curves

DOI10.1007/S12220-008-9024-0zbMath1152.49325OpenAlexW1592749110MaRDI QIDQ942978

Silvano Delladio

Publication date: 8 September 2008

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

Full work available at URL: https://doi.org/10.1007/s12220-008-9024-0

zbMATH Keywords

Hausdorff measureWhitney extension theoremLipschitz maprectifiable setGauss graph

Mathematics Subject Classification ID

Lipschitz (Hölder) classes (26A16) Variational problems in a geometric measure-theoretic setting (49Q20) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Extension of maps (54C20) Hausdorff and packing measures (28A78)

Related Items (4)

Geometric criteria for C1,α$C^{1,\alpha }$‐rectifiability ⋮ A class of one-dimensional geometric variational problem with energy involving the curvature and its derivatives: a geometric measure-theoretic approach ⋮ Functions of class \(C^1\) subject to a Legendre condition in an enhanced density set ⋮ The set of regular values (in the sense of Clarke) of a Lipschitz map. A sufficient condition for rectifiability of class $C^3$

Cites Work

• A result about \(C^3\)-rectifiability of Lipschitz curves
• On the structure of singular sets of convex functions
• Minimizing functionals depending on surfaces and their curvatures: A class of variational problems in the setting of generalized Gauss graphs
• Special generalized Gauss graphs and their application to minimization of functional involving curvatures.
• On hypersurfaces in \(\mathbb{R}^{n+1}\) with integral bounds on curvature.
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