首页/论文/2005.12063

arXiv 2005.120632020-05math.CV

Holomorphic families of Fatou-Bieberbach domains and applications to Oka manifolds

Franc Forstneric, Erlend Fornaess Wold

备注：: A few minor corrections were made. To appear in Math. Res. Lett
发表信息：: Math. Res. Lett. 27(6):1697-1706, 2020
DOI：: 10.4310/MRL.2020.v27.n6.a5

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

A Fatou-Bieberbach domain in C^2 which is not Runge

We give an example of a Fatou-Bieberbach domain which is not Runge in C^2.

2007-08-29math.CV

非Runge的Fatou-Bieberbach域在具有密度性质的Stein流形中

Non-Runge Fatou-Bieberbach Domains in Stein Manifolds with the Density Property

Universität Bern（伯尔尼大学）；Shanghai Jiao Tong University（上海交通大学）

本文研究了在具有密度性质的Stein流形中构造非Runge的Fatou-Bieberbach域的方法，并给出了具体例子。

2026-03-06math.CV

Fatou-Bieberbach domains in $\mathbb C^n\setminus\mathbb R^k$

We construct Fatou-Bieberbach domains in $\mathbb C^n$ for $n>1$ which contain a given compact set $K$ and at the same time avoid a totally real affine subspace $L$ of dimension $<n$, provided that $K\cup L$ is polynomially convex. By using this result, we show that the domain $\mathbb C^n\setminus\mathbb R^k$ for $1\le k<n$ enjoys the Oka property with approximation for maps from any Stein manifold of dimension $<n$.

2014-11-24math.CV

Fatou-Bieberbach domains as basins of attraction of automorphisms tangent to the identity

We prove that there exists an automorphism of C^2 tangent to the identity with a domain of attraction to the origin, biholomorphic to the origin, along a degenerate characteristic direction.

2009-07-12math.CVmath.DS

Fatou-Bieberbach Domains

We show that for any $m\in\NN\cup\{\infty\}$ there exist $m$ disjoint FB domains whose union is dense in $\CC^k$. In fact we show that any point not in the union is a boundary point for all the domains. We construct FB domains that contains arbitrary countable collections of subvarieties of $\CC^k$, and we construct FB domains that intersect elements of countable collections of affine subspaces of $\CC^k$ in connected proper subsets. Moreover, we show that any Runge FB domain is the attracting basin for a sequence of automorphisms of $\CC^k$, although not necessarily if you only allow iteratio…

2005-02-26math.CV

Un domaine de Fatou-Bieberbach \a plusieurs feuillets

We propose, within the context of the dynamics of a holomorphic germ in CI^N, a definition of 'attracting basin' of a fixed point. We prove that the inverse germ of an endomorphism of CI^N with a repulsive fixed point in 0, satisfying a supplementary technical hypothesis, admits an attracting basin which could be described as a Fatou-Bieberbach domain 'with many leaves'.

2003-07-17math.CVmath.DS

更多相关论文收起更多论文

{ \bf C}在{ \bf C} $^2$中的双曲补嵌入

An embedding of {\bf C} in {\bf C}$^2$ with hyperbolic complement

设$X$是$\CC^2$的一个闭的、$1$维的复子簇，$\ol{\BB}$是$\CC^2 - X$中的一个闭球.然后存在具有$X \subseteq Ω\subseteq \CC^2 - \ol{\BB}$的Fatou-Bieberbach域$Ω$和双全纯映射$Φ: Ω\ra \CC^2$，使得$\CC^2 - Φ(X)$是Kobayashi双曲的。作为推论，有一个嵌入的平面在$\CC^2$，其补充是双曲的，有一个非平凡的Fatou-Bieberbach域包含任何有限收集的复杂的线。

1995-06-20math.CVmath.DS

Dynamics of generic endomorphisms of Oka-Stein manifolds

We study the dynamics of a generic endomorphism $f$ of an Oka-Stein manifold $X$. Such manifolds include all connected linear algebraic groups and, more generally, all Stein homogeneous spaces of complex Lie groups. We give several descriptions of the Fatou set and the Julia set of $f$. In particular, we show that the Julia set is the derived set of the set of attracting periodic points of $f$ and that it is also the closure of the set of repelling periodic points of $f$. Among other results, we prove that $f$ is chaotic on the Julia set and that every periodic point of $f$ is hyperbolic. We a…

2021-03-20math.CVmath.DS

周期哈密顿近似与\mathbb{C^2}中的Oka补集

Periodic transport and Oka complements in $\C^n$

Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院数学科学国家重点实验室）；School of Mathematical Sciences, University of Chinese Academy of Sciences（中国科学院大学数学科学学院）

本文结合周期哈密顿输运与吸引盆，证明闭管和闭环带乘积在\mathbb{C^2}中的补集为Oka流形，并构造避开管的Fatou--Bieberbach域族，解决了Forstnerič和Wold关于全实仿射子空间的问题。

2026-10-01math.CV

Oka实现、基本群与上纤维化

Oka realizations, fundamental groups, and holomorphic cofibrations

Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；Faculty of Mathematics, Kyushu University（九州大学数学系）

该研究围绕Oka流形，构造了其复欧氏空间开子集等实现，实现可数群为Oka区域基本群，分类全纯上纤维化并建立分解，明确了相关流形基本群的性质。

2026-10-14math.AGmath.ATmath.CV

代数环面中的冈补及其对数覆盖

Oka complements in algebraic tori and their logarithmic covers

该研究证明代数环面中紧多项式凸集K对应的补集X_K及其对数覆盖Y_K均为Oka集，Y_K还允许指定全纯截面的归一化全纯嵌入族，相关方法可应用于构造多种Oka集的补集。

2026-10-20math.CV

Attracting domains of maps tangent to the identity whose only characteristic direction is non-degenerate

We prove that a holomorphic fixed point germ in two complex variables, tangent to the identity, and whose only characteristic direction is non-degenerate, has a domain of attraction on which the map is conjugate to a translation. In the case of a global automorphism, the corresponding domain of attraction is a Fatou-Bieberbach domain.

2012-02-01math.CVmath.DS

关于Rubel两个参数正常函数问题的解

A Solution to a Problem of Rubel on Two-Parameter Normal Families of Entire Functions

Fudan University（复旦大学）；Xi’an Jiaotong University（西安交通大学）

本文构造了一个整个函数F(z,a,b)∈O(C³)，使其在C上为正常族，而F不通过单一整个参数因子化，解决了Rubel关于Liouville型刚性的问题，并满足更强的条件。

2026-03-21math.CV