Abstract
We make a systematic study of (quasi-)plurisubharmonic envelopes on compact Kähler manifolds, as well as on domains of $\mathbb{C}^n$, by using and extending an approximation process due to Berman [Ber19]. We show that the quasi-plurisubharmonic envelope of a viscosity super-solution is a pluripotential super-solution of a given complex Monge–Ampère equation. We use these ideas to solve complex Monge–Ampère equations by taking lower envelopes of super-solutions.
Funding Statement
The authors are partially supported by the ANR project GRACK.
Citation
Vincent Guedj. Chinh H. Lu. Ahmed Zeriahi. "Plurisubharmonic envelopes and supersolutions." J. Differential Geom. 113 (2) 273 - 313, October 2019. https://doi.org/10.4310/jdg/1571882428
