Quasi-plurisubharmonic envelopes 1: uniform estimates on Kähler manifolds
Vincent Guedj
Université de Toulouse, Toulouse, FranceChinh H. Lu
Université d’Angers, Angers, France
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Abstract
We develop a new approach to a priori -estimates for degenerate complex Monge–Ampère equations on complex manifolds. It only relies on compactness and envelopes properties of quasi-plurisubharmonic functions. Our method allows one to obtain new and efficient proofs of several fundamental results in Kähler geometry. In a sequel we shall explain how this approach also applies to the hermitian setting, producing new relative a priori bounds, as well as existence results.
Cite this article
Vincent Guedj, Chinh H. Lu, Quasi-plurisubharmonic envelopes 1: uniform estimates on Kähler manifolds. J. Eur. Math. Soc. (2024), published online first
DOI 10.4171/JEMS/1460