Document Type
Article
Date of Original Version
2013
Department
Mathematics
Abstract
We consider the convergence of pointed multiply connected domains in the Carathéodory topology. Behaviour in the limit is largely determined by the properties of the simple closed hyperbolic geodesics which separate components of the complement. Of particular importance are those whose hyperbolic length is as short as possible which we call meridians of the domain. We prove continuity results on convergence of such geodesics for sequences of pointed hyperbolic domains which converge in the Carathéodory topology to another pointed hyperbolic domain. Using these we describe an equivalent condition to Carathéodory convergence which is formulated in terms of Riemann mappings to standard slit domains.
Citation/Publisher Attribution
Comerford, M. (2013). The Carathéodory topology for multiply connected domains I. Open Mathematics, 11(2), 322-340. doi: 10.2478/s11533-012-0136-1
Available at: https://doi.org/10.2478/s11533-012-0136-1
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.