Potential theory on complex projective space: Application to characterization of pluripolar sets and growth of analytic varieties
Potential theory on complex projective space: Application to characterization of pluripolar sets and growth of analytic varieties
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复射影空间势理论：在多极集表征和解析簇增长中的应用
DOI：
10.1215/ijm/1256046156
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发表时间：
1984
影响因子：
0.6
通讯作者：
R. Molzon
中科院分区：
文献类型：
--
作者：
R. Molzon
如果对于每个点E E存在p的邻域U和U上定义的多重次调和函数，使得EC U Ix b(x) oo在U的每个分量上不等于oo，则称集合ECPnC是局部多极的。Alexander在他的关于投影容量[1]的论文中，给出了PnC中用Tchebycheff常数z(E)表示的多极集的表征。他的定理说当且仅当z(E)为0时E是局部多极的。常数z(E)由PnC上的归一化齐次多项式定义。最近贝德福德和泰勒给出了多极集的另一个特征。它们的表征涉及蒙日-安培方程和一组ECC的“平衡”。在本文中，我给出了P 'C中关于概率测度的奇异积分的一个局部多极集的刻划，其支持在E上；有问题的集合。这个奇异积分的核定义在
A set ECPnC is said to be locally pluripolar if for each pointp E E there exists a neighborhood U of p and a plurisubharmonic function defined on U such that E C U Ix b(x) oo and is not identically oo on each component of U. A basic problem in function theory of several complex variables is to characterize those sets which are pluripolar. In his paper on projective capacity [1], Alexander gives a characterization of pluripolar sets in PnC in terms of a Tchebycheff constant z(E). His theorem says that E is locally pluripolar if and only if z(E) 0. The constant z(E) is defined in terms of normalized homogeneous polynomials on PnC. Another characterization of pluripolar sets was recently given by Bedford and Taylor [3]. Their characterization involves the Monge-Ampere equation and a "balayage" for a set ECC. In this paper I give a characterization of locally pluripolar sets in P’C in terms of a singular integral with respect to a probability measure, supported on E; the set in question. The kernel of this singular integral is defined on