Riemann mapping theorem in $\mathbb{C}^{n}$
Volume 106 / 2012
Annales Polonici Mathematici 106 (2012), 199-206
MSC: Primary 46J15; Secondary 46E15.
DOI: 10.4064/ap106-0-15
Abstract
The classical Riemann Mapping Theorem states that a nontrivial simply connected domain $\varOmega$ in $\mathbb{C}$ is holomorphically homeomorphic to the open unit disc $\mathbb{D}$. We also know that “similar” one-dimensional Riemann surfaces are “almost” holomorphically equivalent.
We discuss the same problem concerning “similar” domains in $\mathbb{C}^{n}$ in an attempt to find a multidimensional quantitative version of the Riemann Mapping Theorem
