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arXiv · 2106.04273

Quasi-plurisubharmonic envelopes 1: Uniform estimates on K\"ahler manifolds

Vincent Guedj·Chinh H. Lu
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Abstract

We develop a new approach to $L^{\infty}$-a priori estimates for degenerate complex Monge-Amp\`ere 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 K\"ahler 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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Vincent Guedj, Chinh H. Lu. 2021-06-08. Quasi-plurisubharmonic envelopes 1: Uniform estimates on K\"ahler manifolds. https://arxiv.org/abs/2106.04273

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