Partial pluricomplex energy and integrability exponents of plurisubharmonic functions
https://doi.org/10.1016/j.aim.2009.07.002Publisher, magazine: ,
Publication year: 2009
Lưu Trích dẫn Chia sẻAbstract
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.