AN OPTIMAL L~2 EXTENSION THEOREM ON WEAKLY PSEUDOCONVEX K?HLER MANIFOLDS

摘要

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