Arkiv för Matematik

Volume 60 (2022)

Number 2

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

Pages: 323 – 333

DOI: https://dx.doi.org/10.4310/ARKIV.2022.v60.n2.a5

Authors

G.D. Di Salvo (Department of Mathematics, University of Oslo, Norway)

E.F. Wold (Department of Mathematics, University of Oslo, Norway)

Abstract

We prove that there exist Cantor sets of arbitrarily large $2$-dimensional Lebesgue measure whose complements admit proper holomorphic embeddings in $\mathbb{C}^2$.

2010 Mathematics Subject Classification

32E20

Received 14 December 2021

Received revised 23 February 2022

Accepted 5 April 2022

Published 26 October 2022