Acta mathematica scientia, Series B >
LELONG-DEMAILLY NUMBERS IN TERMS OF CAPACITY AND WEAK CONVERGENCE FOR CLOSED POSITIVE CURRENTS
Received date: 2012-05-10
Revised date: 2012-11-02
Online published: 2013-11-20
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) = ∫K T ^ (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.
Key words： positive current; capacity
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 . DOI: 10.1016/S0252-9602(13)60112-5
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