Complex analysis of Bergman spaces and α-cohomology

Bergman metric of bounded balanced pseudoconvex domains in C-D1n-D1 was studied。一个定量的结果将对Jarnicki的完美的第一次约会--Pflug被发现了。Singular Fiber metric was used to obtain as Estimate for the Bergman kernel function on pseudoconvex domains in Py D1n Py D1. A new phenomenon encountere that local hyperconvex domains in py D1n py d1 are not necessarily globally hyperconvex. As for the domains with smooth boundary existence of bounded p.s.h.该功能已提供。在这种情况下，边界是真实的分析，它证明了这样一个伪convex域必须严格地在某些边界点。最近，一个Ly D12 y D1扩展理论的通用化到复杂的Manifolds已经出现，它是，作为一个corollary，一个著名的Ly D12 y D1分区理论的Skoda。

Bergman metric of bounded balanced pseudoconvex domains in CィイD1nィエD1 was studied. A quantitative result implying the completeness first due to Jarnicki-Pflug was obtained. Singular fiber metric was used to obtain as estimate for the Bergman kernel function on pseudoconvex domains in PィイD1nィエD1. A new phenomenon encountere was that locally hyperconvex domains in PィイD1nィエD1 are not necessarily globally hyperconvex. As for the domains with smooth boundary existence of bounded p.s.h. functions was proved. In case the boundary is real analytic, it was proved that such a pseudoconvex domain must be strictly pseudoconvex at some boundary point. More recently, a generalization of an LィイD12ィエD1 extension theorem to complex manifolds was obtained, which has, as a corollary, a famous LィイD12ィエD1 division theorem of Skoda.