Stein Small Deformations of Strictly Pseudoconvex Surfaces
Stein Small Deformations of Strictly Pseudoconvex Surfaces
复制标题
严格赝凸曲面的 Stein 小变形
DOI：
10.1090/conm/207/02717
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发表时间：
1997
影响因子：
1.1
通讯作者：
B. D. Oliveira
中科院分区：
文献类型：
--
作者：
F. Bogomolov;B. D. Oliveira
本文分析了严格拟凸曲面变形的解析环的性质。作为初步结果，我们证明了一个相对紧的严格伪凸曲面是两个Stein开子集的并集。本文的主要结果是：极小相对紧严格伪凸曲面存在一个小变形，它没有正维解析圈，因此是Stein.我们还证明了严格伪凸曲面包含一个半正则1维圈，如果它包含一个1-dim圈。最后将主要结果应用于三维流形的切触结构的研究。
This article analyses the behaviour of analytic cycles on deforma- tions of strictly pseudoconvex surfaces. As a preliminary result we show that a relatively compact strictly pseudoconvex surface is the union of two Stein open subsets. The main result of the article is that there is a small deforma- tion of a minimal relatively compact strictly pseudoconvex surface that has no positive dimensional analytic cycles, hence is Stein. We also prove that a strictly pseudoconvex surface contains a semiregular 1-dimensional cycle if it contains one 1-dim cycle. In the last section the main result is applied to the study of contact structures of three dimensional manifolds.