Local Indicators for Plurisubharmonic Functions

Pierre Lelong; Alexander Rashkovskii

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Local Indicators for Plurisubharmonic Functions

Pierre Lelong·Alexander Rashkovskii

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Abstract

A notion of local indicator for a plurisubharmonic function is introduced. The indicator is a certain plurisubharmonic function in the unit polydisc, which controls the behavior of the considered function near a fixed point of its singularity, as well as the residual Monge-Ampere mass of the function at this point. A pluricomplex Green function with respect to given indicators is constructed and applied to the Dirichlet problem for the Monge- Ampere operator in the class of plurisubharmonic functions with isolated singularities.

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BibTeX RIS

Pierre Lelong, Alexander Rashkovskii. 1999-01-05. Local Indicators for Plurisubharmonic Functions. https://arxiv.org/abs/math/9901014

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