The Carathéodory topology for multiply connected domains II

• Autorzy: Mark Comerford
• Języki publikacji: EN

Abstrakty

EN

We continue our exposition concerning the Carathéodory topology for multiply connected domains which we began in [Comerford M., The Carathéodory topology for multiply connected domains I, Cent. Eur. J. Math., 2013, 11(2), 322–340] by introducing the notion of boundedness for a family of pointed domains of the same connectivity. The limit of a convergent sequence of n-connected domains which is bounded in this sense is again n-connected and will satisfy the same bounds. We prove a result which establishes several equivalent conditions for boundedness. This allows us to extend the notions of convergence and equicontinuity to families of functions defined on varying domains.

Słowa kluczowe

EN

Carathéodory Topology; Meridians; Bounded family of pointed domains

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: 2014
• Tom: 12
• Numer: 5
• Strony: 721-741

Daty

wydano

2014-05-01

online

2014-02-15

Twórcy

autor

Mark Comerford

• University of Rhode Island

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-013-0365-y