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

Erlend Fornæss Wold; Giovanni Domenico Di Salvo

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arXiv · 2112.07514

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

Erlend Fornæss Wold·Giovanni Domenico Di Salvo

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Abstract

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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Erlend Fornæss Wold, Giovanni Domenico Di Salvo. 2021-12-14. Proper Holomorphic Embeddings of complements of large Cantor sets in $\Bbb C^2$. https://arxiv.org/abs/2112.07514

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