Proper Holomorphic Embeddings of complements of large Cantor sets in $\Bbb C^2$

Erlend Fornæss Wold, Giovanni Domenico Di Salvo

arxiv(2022)

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摘要
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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