2013/07/10 by Zhijian Qiu, Qiu, Zhijian
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1307.2740
openalex publication_date 2013/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a bounded simply connected domain in the complex plane. A point a∈ ∂ G is said to be accessible from inside of G if there is a Jordan arc J such that J⊂ G and J∩∂ G=\a\. In this paper the author shows that a univalent analytic function ψ from the unit disk D onto G extends continuously to D if and only if every a∈∂ G is accessible. The main result covers a famous theorem proved by C. Caratheödory, which says that if G is a Jordan domain, then ψ extends to be a homeomorphism from D onto to G.