On a CR family of compact strongly pseudoconvex CR manifolds
On a CR family of compact strongly pseudoconvex CR manifolds
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DOI：
10.4310/jdg/1143593744
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发表时间：
2006
影响因子：
2.5
通讯作者：
Xiaojun Huang;H. Luk;S. Yau
中科院分区：
文献类型：
--
作者：
Xiaojun Huang;H. Luk;S. Yau
研究了至少5维的紧强伪凸CR流形族的同时填充和嵌入问题。在纤维CR流形的第一Kohn-Rossi上同调群的常维假设下，我们也推导了填充Stein空间中Stein纤维的正规性。我们的方法的两个主要组成部分是Catlin关于在混合边界条件下∂-方程的解的工作，以及Siu和Ling关于复空间(1,1)-凹凸族的Grauert直接像理论的研究。
We study the simultaneous filling and embedding problem for a CR family of compact strongly pseudoconvex CR manifolds of dimension at least 5. We also derive, as a consequence, the normality of the Stein fibers of the filled-in Stein space under the constant dimensionality assumption of the first Kohn-Rossi cohomology group of the fiber CR manifolds. Two main ingredients for our approach are the work of Catlin on the solution of the ∂-equation with mixed boundary conditions and the work of Siu and Ling on the study of the Grauert direct image theory for a (1,1)-convex-concave family of complex spaces.