Families of Proper Holomorphic Embeddings and Carleman-type Theorems with parameters

Giovanni Domenico Di Salvo, Tyson Ritter, Erlend F. Wold

We solve the problem of simultaneously embedding properly holomorphically into ${\mathbb{C}}^2$ a whole family of $n$-connected domains ${\Omega }_r\subset {\mathbb{P}}^1$ such that none of the compone…