The new Neumann operator associated with deformations of strongly pseudo convex domains and its application to deformation theory
The new Neumann operator associated with deformations of strongly pseudo convex domains and its application to deformation theory
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与强赝凸域变形相关的新诺依曼算子及其在变形理论中的应用
DOI：
10.1007/bf01394061
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发表时间：
1982
影响因子：
3.1
通讯作者：
T. Akahori
中科院分区：
文献类型：
--
作者：
T. Akahori
尽管许多有趣的结果有关孤立奇点（参见。[9])除了某些特殊情况外，强伪凸域的变形族的存在性一直是开放的（参见[10]）。另一方面，在强伪凸域的紧边界的情况下，已经取得了很大的进展（参见。[7])”““在Kuranishi的意义上，证明了Kazakhstan家族的存在。[2]）。因此，遵循[2]中成功的方法似乎是自然的。在这项工作中，我们采用了这一点。为了更详细地了解这一点，我们回顾了[2]中的方法。设N是复流形，dim c N> 5，~ 2是N的强伪凸子域.设（F（f ~ 2，T ~ N| AV（T”N）*），~）N）是T 'N-值Dolbeault复形，（F（bQ，T'|第176章是他的阴谋然后，[2]中的方法由三部分组成：
In spite of many interesting results related to isolated singularities (cf.[9]), the existence of the versal family of deformations of the strongly pseudo convex domains has been left open except some special cases (cf.[10]). On the other hand, in the case of compact boundaries of strongly pseudo convex domains much progress has been made (cf.[7]) and the existence of the versal family (in a sense of Kuranishi) was proved (cf.[2]). Therefore it seems natural to follow the approach in [2] which was successful. In this work, we adopt this. To see this in more detail, we recall the approach in [2]. Let N be a complex manifold with dim c N> 5 and~ 2 be a strongly pseudo convex subdomain of N. Let (F (f2, T'N| AV (T" N)*),~) N) be the T'N-valued Dolbeault complex and (F (bQ, T'| 176 be its induced boundary complex. Then, the approach in [2] consists of three parts: