English

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

Complex Variables 2023-06-21 v3

Abstract

We present a construction of a proper holomorphic embedding f ⁣:P1CC2f\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.

Keywords

Cite

@article{arxiv.2112.07514,
  title  = {Proper Holomorphic Embeddings of complements of large Cantor sets in $\Bbb C^2$},
  author = {Erlend Fornæss Wold and Giovanni Domenico Di Salvo},
  journal= {arXiv preprint arXiv:2112.07514},
  year   = {2023}
}