PLURISUBHARMONIC CURRENTS AND THEIR EXTENSION ACROSS ANALYTIC SUBSETS

Some extension problems are considered here for the class of plurisubharmonic currents, i.e. real currents T such that i partial derivative partial derivativeBAR T is positive. In particular we prove the following theorem: ''Let OMEGA be an open subset of C(N) and Y an analytic subset of OMEGA. Suppose T is a negative plurisubharmonic current on OMEGA - Y of bidimension (p, p); if dim Y < p, then T extends across Y to a plurisubharmonic current on OMEGA.''. For p = N, this is the classical result of Grauert and Remmert on the extension of plurisubharmonic functions.