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.
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页码：1371 / 1412
页数：42
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