An optimal $L^2$ extension theorem on weakly pseudoconvex Kähler manifolds

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.