An optimal \(L^2\) extension theorem on weakly pseudoconvex Kähler manifolds. (English) Zbl 1426.53082

Zhou, Xiangyu; Zhu, Langfeng

J. Differ. Geom. 110, No. 1, 135-186 (2018).

Summary: 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.

MSC:

53C55	Global differential geometry of Hermitian and Kählerian manifolds
32Q15	Kähler manifolds
32L05	Holomorphic bundles and generalizations
32T27	Geometric and analytic invariants on weakly pseudoconvex boundaries

Keywords:

optimal \(L^2\) extension; singular Hermitian metric; plurisubharmonic function; weakly pseudoconvex manifold; Kähler manifold