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

被引：53

作者：

Azzam, Jonas ^{[1
]}

Tolsa, Xavier ^{[1
,2
]}

机构：

[1] Univ Autonoma Barcelona, Dept Matemat, Barcelona 08193, Catalonia, Spain

[2] ICREA, Barcelona, Spain

来源：

GEOMETRIC AND FUNCTIONAL ANALYSIS | 2015年 / 25卷 / 05期

基金：

欧洲研究理事会;

关键词：

FUNDAMENTAL GEOMETRICAL PROPERTIES; MEASURABLE PLANE SETS; ANALYTIC CAPACITY; CURVATURE; SUBSETS; CURVES;

D O I：

10.1007/s00039-015-0334-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that a Radon measure in which is absolutely continuous with respect to the n-dimensional Hausdorff measure is n-rectifiable if the so called Jones' square function is finite -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 . 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.

引用

页码：1371 / 1412

页数：42

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