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Partial pluricomplex energy and integrability exponents of plurisubharmonic functions |
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| Authors: | P hag U Cegrell S Ko&#x;odziej HH Pha&#x;m A Zeriahi |
| Institution: | aDepartment of Mathematics and Mathematical Statistics, Umeå University, SE-901 87 Umeå, Sweden;bJagiellonian University, Institute of Mathematics, Łojasiewicza 6, 30-348 Kraków, Poland;cDepartment of Mathematics, Truong Dai Hoc Su Pham, 136 Xuan Thuy, Cau Giay, Hanoi, Viet Nam;dUniversité Paul Sabatier, Institut de Mathématiques, 118 Route de Narbonne, 31062 Toulouse cedex, France |
| 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. |
| Keywords: | Plurisubharmonic functions Pluricomplex Monge– Ampè re energy Volume of the sublevel sets Exponents of integrability Log canonical thresholds |
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