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September 2018 An optimal $L^2$ extension theorem on weakly pseudoconvex Kähler manifolds
Xiangyu Zhou, Langfeng Zhu
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J. Differential Geom. 110(1): 135-186 (September 2018). DOI: 10.4310/jdg/1536285628

Abstract

In this paper, we prove an $L^2$ extension theorem for holomorphic sections of holomorphic line bundles equipped with singular metrics on weakly pseudoconvex Kähler manifolds. Furthermore, in our $L^2$ estimate, optimal constants corresponding to variable denominators are obtained. As applications, we prove an $L^q$ extension theorem with an optimal estimate on weakly pseudoconvex Kähler manifolds and the log-plurisubharmonicity of the fiberwise Bergman kernel in the Kähler case.

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Xiangyu Zhou. Langfeng Zhu. "An optimal $L^2$ extension theorem on weakly pseudoconvex Kähler manifolds." J. Differential Geom. 110 (1) 135 - 186, September 2018. https://doi.org/10.4310/jdg/1536285628

Information

Received: 22 February 2016; Published: September 2018
First available in Project Euclid: 7 September 2018

zbMATH: 06933733
MathSciNet: MR3851746
Digital Object Identifier: 10.4310/jdg/1536285628

Keywords: Kähler manifold , optimal $L^2$ extension , plurisubharmonic function , singular Hermitian metric , weakly pseudoconvex manifold

Rights: Copyright © 2018 Lehigh University

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Vol.110 • No. 1 • September 2018
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