We show that the symmetrized bidisc 𝔾₂ = {(λ₁+λ₂,λ₁λ₂):|λ₁|,|λ₂| < 1} ⊂ ℂ² cannot be exhausted by domains biholomorphic to convex domains.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap83-2-9,
author = {Armen Edigarian},
title = {A note on Costara's paper},
journal = {Annales Polonici Mathematici},
volume = {83},
year = {2004},
pages = {189-191},
zbl = {1098.32006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap83-2-9}
}
Armen Edigarian. A note on Costara's paper. Annales Polonici Mathematici, Tome 83 (2004) pp. 189-191. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap83-2-9/