论文标题
FATOU-BIEBERBACH域和OKA歧管应用的全体形态家庭
Holomorphic families of Fatou-Bieberbach domains and applications to Oka manifolds
论文作者
论文摘要
我们在任何紧凑的多项式凸子集$ k $ of $ \ mathbb c^n $ for $ n> 1 $的补充中，构建了带有给定中心的FATOU-BIEBERBACH域的不同家族。这为Yuta Kusakabe的最新结果提供了一个简单的证明，其效果是补充$ \ mathbb c^n \ setMinus k $的任何多项式凸出子集$ k $ of $ \ mathbb c^n $都是OKA歧管。类似的结果是用$ \ mathbb c^n $获得的，由任何用密度属性的Stein歧管代替。
We construct holomorphically varying families of Fatou-Bieberbach domains with given centres in the complement of any compact polynomially convex subset $K$ of $\mathbb C^n$ for $n>1$. This provides a simple proof of the recent result of Yuta Kusakabe to the effect that the complement $\mathbb C^n\setminus K$ of any polynomially convex subset $K$ of $\mathbb C^n$ is an Oka manifold. The analogous result is obtained with $\mathbb C^n$ replaced by any Stein manifold with the density property.
