Title: Truncated tube domains with multi-sheeted envelope Show Chinese title

Title: 截断的管状区域与多叶包络

Abstract: The present article is concerned with a group of problems raised by J. Noguchi and M. Jarnicki/P. Plug, namely whether the envelopes of holomorphy of truncated tube domains are always schlicht, i.e. subdomains of $\mathbb{C^n}$, and how to characterize schlichtness if this is not the case. By way of a counter-example homeomorphic to the 4-ball, we answer the first question in the negative. Moreover, it is possible that the envelopes have arbitrarily many sheets. The article is concluded by sufficient conditions for schlichtness in complex dimension two. Show Chinese abstract

Abstract: 本文关注的是由J. Noguchi和M. Jarnicki/P. Plug提出的一组问题，即截断圆柱域的全纯包是否总是单叶的，即$\mathbb{C^n}$的子域，以及如果这不是情况，如何表征单叶性。通过一个与4球面同胚的反例，我们对第一个问题给出了否定回答。此外，全纯包可能具有任意多的页。文章最后给出了复数维数为二时单叶性的充分条件。