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October 2019 Plurisubharmonic envelopes and supersolutions
Vincent Guedj, Chinh H. Lu, Ahmed Zeriahi
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J. Differential Geom. 113(2): 273-313 (October 2019). DOI: 10.4310/jdg/1571882428

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

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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

Information

Received: 18 May 2017; Published: October 2019
First available in Project Euclid: 24 October 2019

zbMATH: 07122209
MathSciNet: MR4023293
Digital Object Identifier: 10.4310/jdg/1571882428

Rights: Copyright © 2019 Lehigh University

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Vol.113 • No. 2 • October 2019
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