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• W2795570865 abstract "We say a measure is $C^{1,alpha}$ $d$-rectifiable if there is a countable union of $C^{1,alpha}$ $d$-surfaces whose complement has measure zero. We provide sufficient conditions for a Radon measure in $mathbb{R}^n$ to be $C^{1,alpha}$ $d$-rectifiable, with $alpha in (0,1]$. The conditions involve a Bishop-Jones type square function and all statements are quantitative in that the $C^{1,alpha}$ constants depend on such a function. Along the way we also give sufficient conditions for $C^{1,alpha}$ parametrizations for Reifenberg flat sets in terms of the same square function. Key tools for the proof come from David and Toro's Reifenberg parametrizations of sets with holes in the Holder and Lipschitz categories." @default.
• W2795570865 created "2018-04-13" @default.
• W2795570865 creator A5005607755 @default.
• W2795570865 date "2017-09-18" @default.
• W2795570865 modified "2023-09-27" @default.
• W2795570865 title "Sufficient conditions for $C^{1,alpha}$ parametrization and rectifiability" @default.
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• W2795570865 hasPublicationYear "2017" @default.
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