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

DOI: 10.12677/PM.2016.62015, PP. 103-110

Keywords: Lelong数，特殊Lagrangian calibration，φ-多次下调和函数，φ-闭正流
Lelong Number, Special Lagrangian Calibration, φ-Plurisubharmonic Function, φ-Positive Closed Current

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Abstract:

本文给出了Cⁿ上φ-闭正流dd^φf的Lelong数，这里φ是特殊Lagrangian calibration，f是L_loc1(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。
In this paper, we give the Lelong number of a φ-positive closed current dd^φf , where φ is the special Lagrangian calibration and f is a φ-plurisubharmonic function in L_loc1(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.

References

[1]	Harvey, R. and Lawson, H. (1982) Calibrated Geometries. Acta Mathematica, 148, 47-157. http://dx.doi.org/10.1007/BF02392726
[2]	Harvey, R. and Lawson, H. (1982) Plurisubharmonic Functions in Calibrated Geometries. http://arxiv.org/abs/math/0601484
[3]	Harvey, R. and Lawson, H. (2009) An Introduction to Potential Theory in Calibrated Geometry. American Journal of Mathematics, 131, 893-944. http://arxiv.org/abs/0710.3920
[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. http://arxiv.org/abs/0710.3921
[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. http://dx.doi.org/10.1512/iumj.2007.56.3209
[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.

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