# Quasi-plurisubharmonic envelopes 3: Solving Monge-Amp\`ere equations on hermitian manifolds

@inproceedings{Guedj2021QuasiplurisubharmonicE3, title={Quasi-plurisubharmonic envelopes 3: Solving Monge-Amp\`ere equations on hermitian manifolds}, author={V. Guedj and Chinh H. Lu}, year={2021} }

We develop a new approach to L-a priori estimates for degenerate complex Monge-Ampère equations on complex manifolds. It only relies on compactness and envelopes properties of quasi-plurisubharmonic functions. In a prequel [GL21a] we have shown how this method allows one to obtain new and efficient proofs of several fundamental results in Kähler geometry. In [GL21b] we have studied the behavior of Monge-Ampère volumes on hermitian manifolds. We extend here the techniques of [GL21a] to the… Expand

#### One Citation

Quasi-plurisubharmonic envelopes 2: Bounds on Monge-Amp\`ere volumes

- Mathematics
- 2021

Abstract. In [GL21a] we have developed a new approach to L∞-a priori estimates for degenerate complex Monge-Ampère equations, when the reference form is closed. This simplifying assumption was used… Expand

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Quasi-plurisubharmonic envelopes 2: Bounds on Monge-Amp\`ere volumes

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Abstract. In [GL21a] we have developed a new approach to L∞-a priori estimates for degenerate complex Monge-Ampère equations, when the reference form is closed. This simplifying assumption was used… Expand

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We develop a new approach to L∞-a priori estimates for degenerate complex Monge-Ampère equations on complex manifolds. It only relies on compactness and envelopes properties of quasi-plurisubharmonic… Expand

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