实流形的复维数、附加解析圆与参数辐角原理
Complex dimensions of real manifolds, attached analytic discs and parametric argument principle
摘要：
设$Ω$是复流形$X$的光滑实解析子流形.本文建立并研究了以下三个主题之间的联系：1）附着解析圆盘光滑族的拓扑性质，$Ω$的流形，2）$Ω$的复切空间维数的下界，3）从标准复圆盘到$X$的全纯映射光滑族的辐角原理的推广.特别地，我们得到了复流形及其边界的附加解析圆盘的特征。当$Ω$是图的特殊情况下，导致新的全纯和$CR$功能的特点，特别是，解决一些开放的问题，这样的功能。
英文摘要：
Let $Ω$ be a smooth real analytic submanifold of a complex manifold $X$. We establish and study the link between the following 3 subjects: 1) topological properties of smooth families of attached analytic discs, the manifold $Ω$ admits, 2) lower bounds for dimensions of complex tangent spaces of $Ω$, 3) a generalization of the argument principle for smooth families of holomorphic mappings from the standard complex disc to $X$. In particular, we obtain characterization of complex manifolds and their boundaries in terms of attached analytic discs. The special case when $Ω$ is the graph, leads to new characterizations of holomorphic and $CR$ functions, and in particular, to solutions of some open problems about such functions.
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