Lelong numbers of $m-$subharmonic functions

Amel Benali; Noureddine Ghiloufi

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arXiv · 1710.03464

Lelong numbers of $m-$subharmonic functions

Amel Benali·Noureddine Ghiloufi

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Abstract

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

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Amel Benali, Noureddine Ghiloufi. 2017-10-10. Lelong numbers of $m-$subharmonic functions. https://arxiv.org/abs/1710.03464

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