Riemann mapping theorem in Cn

Krzysztof Jarosz
2012 Annales Polonici Mathematici  
The classical Riemann Mapping Theorem states that a nontrivial simply connected domain Ω in C is holomorphically homeomorphic to the open unit disc D. We also know that "similar" one-dimensional Riemann surfaces are "almost" holomorphically equivalent. We discuss the same problem concerning "similar" domains in C n in an attempt to find a multidimensional quantitative version of the Riemann Mapping Theorem. 2010 Mathematics Subject Classification: Primary 46J15; Secondary 46E15.
doi:10.4064/ap106-0-15 fatcat:nhg6m4raifeoxnllnqbgehbdiy