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Plurisubharmonic envelopes and supersolutions
Journal of Differential Geometry  (IF2.688),  Pub Date : 2019-10-01, DOI: 10.4310/jdg/1571882428
Vincent Guedj, Chinh H. Lu, Ahmed Zeriahi

We make a systematic study of (quasi-)plurisubharmonic envelopes on compact K\"ahler manifolds, as well as on domains of $\mathbb{C}^n$, by using and extending an approximation process due to Berman [Ber13]. We show that the quasi-psh envelope of a viscosity super-solution is a pluripotential super-solution of a given complex Monge-Amp\`ere equation. We use these ideas to solve complex Monge-Amp\`ere equations by taking lower envelopes of super-solutions.