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

查看全文 作　　者：Fredj [1]ELKHADHRA

机构地区：[1]Institut Suprieur de Gestion de Sousse B.P.n.763,4000 Sousse,Tunisie

出　　处：《Acta Mathematica Scientia》索引2013年第33卷第6期,共15页

摘　　要：In this paper we give a new definition of the Lelong-Demailly number in terms of the CT-capacity,where T is a closed positive current and CT is the capacity associated to T.This derived from some esimate on the growth of the CT-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 CT(K)=∫KT∧(ddcv)p,where K is a compact subset.Finally,we give some conditions on the capacity CT that guarantees the weak convergence ukTk → uT,for positive closed currents T,Tk and psh functions uk,u. 关键词：收敛收电流容量功能特性 CT H函数封闭

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

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