Institute for Mathematical Physics on Compact Complex Spaces L 2 -theory for the ∂-operator on Compact Complex Spaces
Institute for Mathematical Physics on Compact Complex Spaces L 2 -theory for the ∂-operator on Compact Complex Spaces
复制标题
紧复空间数学物理研究所 L 2 -紧复空间上的 ∂ 算子理论
DOI：
--
复制
发表时间：
--
期刊：
影响因子：
--
通讯作者：
J. Ruppenthal
中科院分区：
文献类型：
--
作者：
J. Ruppenthal
在20世纪60年代，L2-算子理论已经成为复分析中一个重要的、不可缺少的部分，并对数学的许多其他领域产生了影响。但是，虽然理论是非常发达的复流形，它一直是一个开放的问题，因为创造一个适当的L2理论的奇异复空间的π-算子。本文在具有孤立奇点的n维紧致复空间上建立了（0，q）和（n，q）-形式的理论。我们的大多数方法也适用于任意奇点和非紧情形。
In the 1960s, the L 2-theory for the ∂-operator has become an important , indispensable part of complex analysis with influence to many other areas of mathematics. But, whereas the theory is very well developed on complex manifolds, it has been an open problem ever since to create an appropriate L 2-theory for the ∂-operator on singular complex spaces. In the present article, we develop such a theory for (0, q) and (n, q)-forms on compact complex spaces of pure dimension n with isolated singularities. Most of our methods apply to arbitrary singularities and non-compact situations, as well.