论文标题
Bochner的管子定理和广义管的简短证明
A brief proof of Bochner's tube theorem and a generalized tube
论文作者
论文摘要
本说明的目的首先是通过使用K. Oka的边界距离定理（1942）来提供新的简短证明古典Bochner Tube Theorem（1938），直接表明可以通过线段连接了管子座的两个点的两个点。然后，我们采用相同的想法来表明，如果一个未征收的域$ \ Mathfrak {d}：= a_1+ia_2 \ to \ mathbf {c}^n $，带有未建立的真实域$ a_j \ to \ mathbf {r}^n $是pseudoconvex，然后是pseudoconvex，然后是$ a_j $ a_j $ a_j $ n is conji and conji an conji and conji an conji and conji conji and conji and conji（定理）。从此结果的角度来看，我们讨论了M. Abe的概括，并给出了一个有限管的示例，该示例超过了$ \ Mathbf {C}^n $，ABE定理不再拥有。目前的方法可能会阐明（仿射）凸的来源。
The aim of this note is firstly to give a new brief proof of classical Bochner's Tube Theorem (1938) by making use of K. Oka's Boundary Distance Theorem (1942), showing directly that two points of the envelope of holomorphy of a tube can be connected by a line segment. We then apply the same idea to show that if an unramified domain $\mathfrak{D}:=A_1+iA_2 \to \mathbf{C}^n$ with unramified real domains $A_j \to \mathbf{R}^n$ is pseudoconvex, then the both $A_j$ are univalent and convex (a generalization of Kajiwara's theorem). From the viewpoint of this result we discuss a generalization by M. Abe with giving an example of a finite tube over $\mathbf{C}^n$ for which Abe's theorem no longer holds. The present method may clarify the point where the (affine) convexity comes from.
