On the extension of PSH currents (Q2738867)

The main result of the paper is the following extension theorem for currents. Let \(A\) be a closed complete pluripolar subset of an open set \(\Omega\subset\mathbb C^n\) and let \(T\) be a negative plurisubharmonic current of bidimension \((p,p)\) on \(\Omega\setminus A\) such that \(\mathcal H_{2p}(\overline{\text{supp }T}\cap A)=0\). Then \(T\) extends to a negative current \(\widetilde T\) on \(\Omega\) and there exists a closed negative current \(S\) supported by \(A\) such that \(d\widetilde T=\widetilde{dT}\), \(\widetilde{dd^cT}=dd^c\widetilde T+S\).