$\mathbb{C}^2$中大康托集补的真全纯嵌入

IF 0.8 4区数学 Q2 MATHEMATICS Arkiv for Matematik Pub Date : 2021-12-14 DOI:10.4310/arkiv.2022.v60.n2.a5

E. F. Wold, G. Salvo

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引用次数: 0

摘要

我们给出了一个固有全纯嵌入$f\冒号\Bbb P^1\set - C\hookrightarrow \Bbb C^2$的构造，其中C是一个康托集，通过从边2的正方形上去掉越来越小的垂直和水平条而得到，允许实现它具有任意接近4的Lebesgue测度。

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Proper holomorphic embeddings of complements of large Cantor sets in $\mathbb{C}^2$

We present a construction of a proper holomorphic embedding $f\colon \Bbb P^1\setminus C\hookrightarrow \Bbb C^2$, where C is a Cantor set obtained by removing smaller and smaller vertical and horizontal strips from a square of side 2, allowing to realize it to have Lebesgue measure arbitrarily close to 4.

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