﻿ Cn上φ-闭正流的Lelong数 The Lelong Number of a φ-Positive Closed Current on Cn

Pure Mathematics
Vol.06 No.02(2016), Article ID:17142,8 pages
10.12677/PM.2016.62015

The Lelong Number of a -Positive Closed Current on

Fang Wang, Qianqian Kang

College of Science and Technology, Zhejiang International Studies University, Hangzhou Zhejiang

Received: Feb. 28th, 2016; accepted: Mar. 11th, 2016; published: Mar. 17th, 2016

ABSTRACT

In this paper, we give the Lelong number of a -positive closed current, where is the special Lagrangian calibration and f is a -plurisubharmonic function in. Using that Lelong number, we generalize the minimum modulus principle for the holomorphic function of one complex variable, and we get an estimate of the low bound for -plurisubharmonic functions.

Keywords:Lelong Number, Special Lagrangian Calibration, -Plurisubharmonic Function, -Positive Closed Current

-闭正流的Lelong数

1. 引言及主要结果

。这里，表示黎曼流形X的余切空间。一个p维的流t，如果对所有具有紧支柱的p-形式，有

(1.1)

(1.2)

(1.3)

(1.4)

(1.5)

(1.6)

2.的Lelong数

(2.1)

3.多次下调和函数的下界估计

，这里，是切空间的一组基。则显然，且

(3.1)

(3.2)

(3.3)

(3.4)

(3.5)

(3.6)

(3.7)

(3.8)

(3.9)

，则公式(1.3)成立。

。由(3.5)知，对任意一点，都会相应的存在一个实数，满足，使得

(3.10)

，及，可得，

The Lelong Number of a φ-Positive Closed Current on Cn[J]. 理论数学, 2016, 06(02): 103-110. http://dx.doi.org/10.12677/PM.2016.62015

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