Partial pluricomplex energy and integrability exponents of plurisubharmonic functions

Authors: Per Åhag, Urban Cegrell, Sławomir Kołodziej, Phạm Hoàng Hiệp, Ahmed Zeriahi,

https://doi.org/10.1016/j.aim.2009.07.002

Publisher, magazine: ,

Publication year: 2009

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Abstract

We first prove a quantitative estimate of the volume of the sublevel sets of a plurisubharmonic function in a hyperconvex domain with boundary values 0 (in a quite general sense) in terms of its Monge–Ampère mass in the domain. Then we deduce a sharp sufficient condition on the Monge–Ampère mass of such a plurisubharmonic function ϕ for exp(−2ϕ) to be globally integrable as well as locally integrable.

Tags: Plurisubharmonic functions; Pluricomplex Monge–Ampère energy; Volume of the sublevel sets; Exponents of integrability; Log canonical thresholds.