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Quasi-plurisubharmonic envelopes 1: Uniform estimates on Kähler manifolds

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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Preprints, Working Papers, ...
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Contributor : Hoang-Chinh Lu Connect in order to contact the contributor
Submitted on : Friday, July 16, 2021 - 12:04:06 PM
Last modification on : Monday, July 4, 2022 - 9:49:17 AM
Long-term archiving on: : Sunday, October 17, 2021 - 6:36:45 PM


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  • HAL Id : hal-03288425, version 1
  • ARXIV : 2106.04273


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



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