The Lelong Number of a φ-Positive Closed Current on Cn

作者: 王 芳 :浙江外国语学院科学技术学院,浙江 杭州 ; 康倩倩 :浙江外国语学院科学技术学院,浙江 杭州;

关键词: Lelong数特殊Lagrangian calibrationφ-多次下调和函数φ-闭正流Lelong Number Special Lagrangian Calibration φ-Plurisubharmonic Function φ-Positive Closed Current

本文给出了Cn上φ-闭正流ddφf的Lelong数,这里φ是特殊Lagrangian calibration,f是Lloc1(Cn)中的φ-多次下调和函数。并且我们应用此Lelong数,将单复变中全纯函数的极小模原理进行了推广,给出了此类φ-多次下调和函数的一个下界估计。

Abstract: In this paper, we give the Lelong number of a φ-positive closed current ddφf , where φ is the special Lagrangian calibration and f is a φ-plurisubharmonic function in Lloc1(Cn) . 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 φ-plurisubharmonic functions.

文章引用: 王 芳 , 康倩倩 (2016) Cn上φ-闭正流的Lelong数。 理论数学, 6, 103-110. doi: 10.12677/PM.2016.62015


[1] Harvey, R. and Lawson, H. (1982) Calibrated Geometries. Acta Mathematica, 148, 47-157.

[2] Harvey, R. and Lawson, H. (1982) Plurisubharmonic Functions in Calibrated Geometries.

[3] Harvey, R. and Lawson, H. (2009) An Introduction to Potential Theory in Calibrated Geometry. American Journal of Mathematics, 131, 893-944.

[4] Harvey, R. and Lawson, H. (2009) Duality of Positive Currents and Pluri-subharmonic Functions in Calibrated Geometry. American Journal of Mathematics, 131, 1211-1240.

[5] Klimek, M. (1991) Pluripotential Theory. Clarendon Press, Oxford and New York.

[6] Demailly, J. (2010) Analytic Methods in Algebraic Geometry. International Press, Some-rville.

[7] Demailly, J. (1993) Monge-Ampere Operators, Lelong Numbers and Intersection Theory. Complex Analysis and Geometry. The University Series in Mathematics, Plenum, New York, 115-193.

[8] Zeriahi, A. (2007) A Minimum Principle for Plurisubharmonic Functions. Indiana University Mathematics Journal, 56, 2671-2696.

[9] Kang, Q.Q. (2015) A Monge-Ampere Type Operator in 2-Dimensional Special Lagrangian Geometry. Italian Journal of Pure and Applied Mathematics, 34, 449-462.