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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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https://hal-universite-paris-saclay.archives-ouvertes.fr/hal-03288425
Contributor : Hoang-Chinh Lu <>
Submitted on : Friday, July 16, 2021 - 12:04:06 PM
Last modification on : Wednesday, July 21, 2021 - 3:47:17 AM

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Quasipshenvelopes1.pdf
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  • HAL Id : hal-03288425, version 1
  • ARXIV : 2106.04273

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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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