2025/02/02 by Bharathi Thiruvengadam, Thiruvengadam, Bharathi, Jaikrishnan Janardhanan +1
Business, Management and Accounting · Mathematics · Social Sciences · #30C35 #30F45 #32H50 #Complex Variables (math.CV) #FOS: Mathematics #Historical Geography and Cartography #Mathematics and Applications #Optics and Image Analysis
paper · pdf · doi:10.48550/arxiv.2502.00650
openalex publication_date 2025/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main objective of this paper is to show that balls under invariant metrics on hyperbolic planar domains are finitely-connected. As applications, we give new and transparent proofs of classical results on conformal mappings of planar domains. In particular, we show that any conformal self-map of a hyperbolic planar domain with three fixed points is the identity. We also give a new and very simple proof of the theorem by Aumann and Carathéodory that states that the isotropy groups of a hyperbolic planar domain are either finite or the domain is simply-connected.