%0 Journal Article
%T Pluricomplex charge at weak singularities
%A Jonas Wiklund
%J Mathematics
%D 2005
%I arXiv
%X Let $u$ be a plurisubharmonic function, defined on a neighbourhood of a point $x,$ such that the complex Monge-Amp\`ere operator is well-defined on $u.$ Suppose also that $u$ has a weak singularity, in the sense that the Lelong number of $u$ at $x$ vanish. Is it true that the residual mass of the measure $(dd^c{u})^n$ vanish at $x$? To our knowledge there is no known example that falsifies the posed question. In this paper some partial results are obtained. We find that for a significant subset of plurisubharmonic functions with well defined Monge-Amp\`ere mass vanishing Lelong number does implies vanishing residual mass of the Monge-Amp\`ere measure.
%U http://arxiv.org/abs/math/0510671v1