Construction of the Riemann Map
Year: 2024
Type: article
Abstract: We do not give the proof of famous Riemann mappings theorem, for every simply connected region in $${\mathbb{C}}$$ C but we give a series of increasingly better approximations of the Riemann map in the Riemann mapping theorem. The idea is to approximate a domain by a polygon using a Whitney decomposition, then use the Schwarz–Christoffel formula to compute the map onto the polygonal approximation, and finally use the Carathéodory convergence theorem to obtain the Riemann map in the limit. The suggested method will have easy and effective applications in practice.
Authors: Peter V. Dovbush, Steven G. Krantz
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,990
OpenAlex ID: W4403159492