Computing boundary extensions of conformal maps part 2

2013/04/06 by Timothy H. McNicholl, T. H. McNicholl, McNicholl, T. H.
Computer Science · Mathematics · #03D78 #03F60 #30C30 #30E10 #54D05 #Complex Variables (math.CV) #Computability, Logic, AI Algorithms #FOS: Mathematics #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #math.CV #msc:03D78 #msc:03F60 #msc:30C30 #msc:30E10 #msc:54D05

paper · pdf · doi:10.48550/arxiv.1304.1915

Formally known as `Conformal maps and domains with jagged edges'

openalex publication_date 2013/04/06 · arxiv created 2014/03/19 · arxiv updated 2014/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown that there is a computable conformal map of the unit disk onto a domain D that has a computable extension to the closure of the unit disk even though the boundary of D is not effectively locally connected. The proof encodes an arbitrary c.e. set into the local connectivity of the boundary of D.

Related

• Computing conformal maps onto circular domains
• A Riemann mapping theorem for two-connected domains in the plane
• Continuous boundary values of conformal maps
• Computable Caratheodory Theory
• Numerical conformal mapping