Pluripolarity of sets with small Hausdorff measure

被引：4

作者：

Labutin, DA ^{[1
]}

机构：

[1] Australian Natl Univ, Ctr Math & Applicat, Canberra, ACT 0200, Australia

来源：

MANUSCRIPTA MATHEMATICA | 2000年 / 102卷 / 02期

关键词：

Mathematics Subject Classification (1991):32F05;

D O I：

10.1007/s002291020163

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that any set E subset of C-n, n greater than or equal to 2, with finite Hausdorff measure Lambda ((log 1/r)-n) (E) < + infinity is pluripolar. The result is sharp with respect to the measuring function. The new idea in the proof is to combine a construction from potential theory, related to the real variational integral integral(Omega)\del u \(m), Omega subset of R-m, with properties of the piuricomplex relative extremal function for the Bedford-Taylor capacity.

引用

页码：163 / 167

页数：5

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