Year: 1973
Type: article
Abstract: Classically, the Riemann mapping theorem states that any open, simply connected and proper subset of U of the complex plane is analytically equivalent to the open unit disk S(0,1).However this theorem is not constructively valid without some additional restriction on U. Two separate geometric conditions, mappability and maximal extensibility, on U are then proposed.The two conditions are shown to be mathematically equivalent.Finally the mappability condition is shown to be both necessary and sufficient for an analytic equivalence to exist constructively between U and S(0,1).The mappability condition is due Errett Bishop.The sufficiency proof is based on methods contained in [1].
Source: Pacific Journal of Mathematics
Author: Henry Cheng
Institution: University of Southern California
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2041337510