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

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
Full Text: