Existence of Lelong numbers of positive plurisuperharmonic currents
The main result of this paper is the following: Let \(\Omega\) be an open subset of \(\mathbb C^n\) and \(T\) be a positive plurisuperharmonic \((i\partial\overline\partial T\leq 0)\) current of bidimension \((p,p)\) on \(\Omega\), where \(0<p<n\). Then, there exists a pluripolar subset \(E_T\) of \(\Omega\) such that the Lelong number \(\nu_T(z)\) exists for every \(z\in\Omega\smallsetminus E_T\). Moreover, if \(z\in\Omega\) such that \(\nu_T(z)\) exists then it does not depend on the system of coordinates. As an application, the author proves a result on the geometric structure of a positive plurisuperharmonic current and studies the existence of the current \(T=i\partial u\wedge\overline\partial u\) and its Lelong number, where \(u\) is a plurisubharmonic function.
scientific article; zbMATH DE number 6536790