发表机构
University of Ljubljana; Institute of Mathematics, Physics and Mechanics; Adelaide University（卢布尔雅那大学; 数学、物理与力学研究所; 阿德莱德大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究偶数维开流形上Stein结构的连续族，定义驯顺性并分析保持该性质的构造，给出新的驯顺Stein族例子，其满足Oka原理。
AI 中文摘要
设 \\(X\\) 为偶数维光滑开流形，\\(T\\) 为拓扑空间，\\(\{J_t\}_{t\in T}\\) 为 \\(X\\) 上光滑可积Stein结构的连续族。若 \\(X\\) 中任何紧集的 \\(J_t\\)-凸包关于 \\(t\in T\\) 是上半连续的，则称该族为驯顺的。最近研究表明，驯顺Stein族具有良好的函数论性质；特别地，它们满足到任何Oka流形的全纯映射族的Oka原理。我们分析了Stein流形上保持族驯顺性的若干构造与运算，并展示了几个概念上新的驯顺Stein族的例子。
英文摘要
Let \(X\) be a smooth open manifold of even dimension, \(T\) be a topological space, and \(\{J_t\}_{t\in T}\) be a continuous family of smooth integrable Stein structures on \(X\). The family is said to be tame if the \(J_t\)-convex hulls of any compact set in \(X\) are upper semicontinuous with respect to \(t\in T\). It was recently shown that tame Stein families have good function-theoretic properties; in particular, they satisfy the Oka principle for families of holomorphic maps to any Oka manifold. We analyse some constructions and operations on Stein manifolds that preserve tameness of families and we exhibit several conceptually new examples of tame Stein families.
CommentsThis version contains a few minor corrections. In particular, Corollary 1.4 in V1 has been replaced by Proposition 1.3 and Problem 1.5
