Quasi-plurisubharmonic envelopes 1: Uniform estimates on Kähler manifolds

Vincent Guedj (1) , Chinh H. Lu (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 LMO - Laboratoire de Mathématiques d'Orsay

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.

Domains: Mathematics [math]

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