An extremal problem for generalized Lelong numbers

2009/03/04 by Alexander Rashkovskii, Rashkovskii, Alexander
Mathematics · #13H15 #32U05 #32U25 #32U35 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #math.CV #msc:13H15 #msc:32U05 #msc:32U25 #msc:32U35

paper · pdf · doi:10.48550/arxiv.0903.0849

22 pages; final version, to appear in Math. Z

openalex publication_date 2009/03/04 · arxiv created 2009/07/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We look for pointwise bounds on a plurisubharmonic function near its singularity point, given the value of its generalized Lelong number with respect to a plurisubharmonic weight. To this end, an extremal problem is considered. In certain cases, the problem is solved explicitly.

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