Characterization of n-rectifiability in terms of Jones’ square function: Part II

Jonas Azzam, Xavier Tolsa

Research output: Contribution to journalArticleResearchpeer-review

28 Citations (Scopus)

Abstract

© 2015, Springer Basel. We show that a Radon measure μ in Rd which is absolutely continuous with respect to the n-dimensional Hausdorff measure Hn is n-rectifiable if the so called Jones’ square function is finite μ-almost everywhere. The converse of this result is proven in a companion paper by the second author, and hence these two results give a classification of all n-rectifiable measures which are absolutely continuous with respect to Hn. Further, in this paper we also investigate the relationship between the Jones’ square function and the so called Menger curvature of a measure with linear growth, and we show an application to the study of analytic capacity.
Original languageEnglish
Pages (from-to)1371-1412
JournalGeometric and Functional Analysis
Volume25
Issue number5
DOIs
Publication statusPublished - 1 Oct 2015

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