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arxiv: 1703.05254 · v1 · pith:7XUGDG2Qnew · submitted 2017-03-15 · 🧮 math.CV · math.AP· math.DG

Plurisubharmonic envelopes and supersolutions

Vincent Guedj , Chinh H. Lu , Ahmed Zeriahi This is my paper
classification 🧮 math.CV math.APmath.DG
keywords envelopescomplexmonge-ampplurisubharmonicsuper-solutionahlerapproximationber13
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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.

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