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# Plurisubharmonic envelopes and supersolutions

Abstract : 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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https://hal.archives-ouvertes.fr/hal-01890198
Contributor : Hoang-Chinh Lu <>
Submitted on : Tuesday, July 27, 2021 - 8:08:20 PM
Last modification on : Thursday, July 29, 2021 - 4:01:46 AM

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GLZ_Envelopes_JDG.pdf
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### Identifiers

• HAL Id : hal-01890198, version 1
• ARXIV : 1703.05254

### Citation

Vincent Guedj, Chinh H. Lu, Ahmed Zeriahi. Plurisubharmonic envelopes and supersolutions. 2021. ⟨hal-01890198⟩

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