Lelong numbers of m-subharmonic functions

2017/10/10 by Amel Benali, Benali, Amel, Noureddine Ghiloufi +1
Mathematics · #32U05 #32U25 #32U40 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:32U05 #msc:32U25 #msc:32U40

paper · pdf · doi:10.48550/arxiv.1710.03464

arxiv created 2017/10/10 · arxiv updated 2017/10/11

Abstract

In this paper we study the existence of Lelong numbers of m-subharmonic currents of bidimension (p,p) on an open subset of \Bbb Cⁿ, when m+p≥ n. In the special case of m-subharmonic function φ, we give a relationship between the Lelong numbers of dd^cφ and the mean values of φ on spheres or balls. As an application we study the integrability exponent of φ. We express the integrability exponent of φ in terms of volume of sub-level sets of φ and we give a link between this exponent and its Lelong number.

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