LELONG-DEMAILLY NUMBERS IN TERMS OF CAPACITY AND WEAK CONVERGENCE FOR CLOSED POSITIVE CURRENTS

doi:10.1016/S0252-9602(13)60112-5

Abstract

Abstract:

In this paper we give a new definition of the Lelong-Demailly number in terms of the C_T -capacity, where T is a closed positive current and C_T is the capacity associated to T. This derived from some esimate on the growth of the C_T-capacity of the sublevel sets of a weighted plurisubharmonic (psh for short) function. These estimates enable us to give
another proof of the Demailly´s comparaison theorem as well as a generalization of some results due to Xing concerning the characterization of bounded psh functions. Another problem that we consider here is related to the existence of a psh function v that satisfies the equality C_T (K) = ∫_KT ^ (dd^cv)^p, where K is a compact subset. Finally, we give some conditions on the capacity C_T that guarantees the weak convergence u_kT_k → uT, for positive closed currents T, T_k and psh functions u_k, u.

Key words: positive current, capacity

CLC Number:

32C30

Fredj ELKHADHRA. LELONG-DEMAILLY NUMBERS IN TERMS OF CAPACITY AND WEAK CONVERGENCE FOR CLOSED POSITIVE CURRENTS[J].Acta mathematica scientia,Series B, 2013, 33(6): 1652-1666.

Trendmd

[1]	Veli Shakhmurov. ABSTRACT CAPACITY OF REGIONS AND COMPACT EMBEDDING WITH APPLICATIONS [J]. Acta mathematica scientia,Series B, 2011, 31(1): 49-67.
[2]	CHEN Zhen-Long, LI Hui-Qiong. POLAR SETS OF MULTIPARAMETER BIFRACTIONAL BROWNIAN SHEETS [J]. Acta mathematica scientia,Series B, 2010, 30(3): 857-872.
[3]	Chen Zhenlong. GENERALIZED BROWNIAN SHEET IMAGES AND BESSEL-RIESZ CAPACITY [J]. Acta mathematica scientia,Series B, 2007, 27(1): 77-91.
[4]	Yang Chao; Zhang Jianzhong. ON THE BOTTLENECK CAPACITY EXPANSION PROBLEMS ON NETWORKS [J]. Acta mathematica scientia,Series B, 2006, 26(2): 202-208.
[5]	ZHENG Shen-Zhou, KANG Xiu-Yang. THE COMPARISON OF GREEN FUNCTION \|FOR QUASI-LINEAR ELLIPTIC EQUATION [J]. Acta mathematica scientia,Series B, 2005, 25(3): 470-480.
[6]	Lu Guang-Cun. THE WEINSTEIN CONJECTURE ON C1-SMOOTH HYPERSURFACE OF CONTACT TYPE [J]. Acta mathematica scientia,Series B, 2002, 22(4): 557-563.
[7]	YANG Chao, CHEN Xue-Qi. AN INVERSE MAXIMUM CAPACITY PATH PROBLEM WITH LOWER BOUND CONSTRAINTS [J]. Acta mathematica scientia,Series B, 2002, 22(2): 207-212.
[8]	YANG Chao, LIU Jing-Lin. A CAPACITY EXPANSION PROBLEM WITH BUDGET CONSTRAINT AND BOTTLENECK LIMITATION [J]. Acta mathematica scientia,Series B, 2001, 21(3): 428-432.
[9]	Luo Shunlong. COLLISION AND MEETING OF STABLE PROCESSES [J]. Acta mathematica scientia,Series B, 1996, 16(3): 271-278.
[10]	Liu Luqin. THE EQUILIBRIUM PROBLEM AND CAPACITY FOR JUMP MARKOV PROCESSES [J]. Acta mathematica scientia,Series B, 1995, 15(1): 15-30.

LELONG-DEMAILLY NUMBERS IN TERMS OF CAPACITY AND WEAK CONVERGENCE FOR CLOSED POSITIVE CURRENTS

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 10

Metrics

Comments

Recommended 10