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 ℂⁿ in an attempt to find a multidimensional quantitative version of the Riemann Mapping Theorem
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap106-0-15, author = {Krzysztof Jarosz}, title = {Riemann mapping theorem in Cn}, journal = {Annales Polonici Mathematici}, volume = {105}, year = {2012}, pages = {199-206}, zbl = {1269.46032}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap106-0-15} }
Krzysztof Jarosz. Riemann mapping theorem in ℂⁿ. Annales Polonici Mathematici, Tome 105 (2012) pp. 199-206. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap106-0-15/