The Carathéodory topology for multiply connected domains I

• Autorzy: Mark Comerford
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Carathéodory topology; Hyperbolic geodesics; Meridians

Kategorie tematyczne

• 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
• 30C20: Conformal mappings of special domains
• 30C75: Extremal problems for conformal and quasiconformal mappings, other methods

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 2
• Strony: 322-340

Daty

wydano

2013-02-01

online

2012-11-21

Twórcy

autor

Mark Comerford

• University of Rhode Island

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-012-0136-1