Quasi-plurisubharmonic envelopes 3: Solving Monge-Amp\`ere equations on hermitian manifolds - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2021

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

Résumé

We develop a new approach to $L^{\infty}$-a priori estimates for degenerate complex Monge-Amp\`ere equations on complex manifolds. It only relies on compactness and envelopes properties of quasi-plurisubharmonic functions. In a prequel \cite{GL21a} we have shown how this method allows one to obtain new and efficient proofs of several fundamental results in K\"ahler geometry. In \cite{GL21b} we have studied the behavior of Monge-Amp\`ere volumes on hermitian manifolds. We extend here the techniques of \cite{GL21a} to the hermitian setting and use the bounds established in \cite{GL21b}, producing new relative a priori estimates, as well as several existence results for degenerate complex Monge-Amp\`ere equations on compact hermitian manifolds.

Dates et versions

hal-04011556 , version 1 (02-03-2023)

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Vincent Guedj, Chinh H. Lu. Quasi-plurisubharmonic envelopes 3: Solving Monge-Amp\`ere equations on hermitian manifolds. 2023. ⟨hal-04011556⟩
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