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2021 Characterizations of countably $n$-rectifiable radon measures by higher-dimensional Menger curvatures
Max Goering
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Real Anal. Exchange 46(1): 1-36 (2021). DOI: 10.14321/realanalexch.46.1.0001

Abstract

We provide a characterization of countably n-rectifiable measures in terms of $\sigma$-finiteness of the integral Menger curvature. We also prove that a finiteness condition on pointwise Menger curvature can characterize rectifiability of Radon measures. Motivated by the partial converse of Meurer's work by Kolasiński we prove that under suitable density assumptions there is a comparability between pointwise-Menger curvature and the sum over scales of the centered $\beta$-numbers at a point.

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Max Goering. "Characterizations of countably $n$-rectifiable radon measures by higher-dimensional Menger curvatures." Real Anal. Exchange 46 (1) 1 - 36, 2021. https://doi.org/10.14321/realanalexch.46.1.0001

Information

Published: 2021
First available in Project Euclid: 14 October 2021

Digital Object Identifier: 10.14321/realanalexch.46.1.0001

Subjects:
Primary: 28A75 , 53A07
Secondary: 28A78

Keywords: higher codimension , Menger curvature , rectifiability

Rights: Copyright © 2021 Michigan State University Press

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Vol.46 • No. 1 • 2021
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