Embeddings of infinitely connected planar domains into C^2
  We prove that every circled domain in the Riemann sphere admits a proper holomorphic embedding to C^2. Our methods also apply to circled domains with punctures, provided that all but finitely many of the punctures belong to the closure of the set of complementary discs. 
Franc Forstneric and Erlend Fornaess Wold
math.CV