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Quasi-plurisubharmonic envelopes 1: Uniform estimates on Kähler manifolds

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Abstract

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. Our method allows one to obtain new and efficient proofs of several fundamental results in Kähler geometry as we explain in this article. 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.
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hal-03288425 , version 1 (16-07-2021)

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Vincent Guedj, Chinh H. Lu. Quasi-plurisubharmonic envelopes 1: Uniform estimates on Kähler manifolds. 2021. ⟨hal-03288425⟩
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