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On the Weakness of Some Boundary Component

Published online by Cambridge University Press:  22 January 2016

Tohru Akaza
Tohru Akaza*
Affiliation:
Mathematical Institute, Kanazawa University
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Let D be a domain in the complex z-plane and γ be a boundary component of D consisting of a single point. The component γ is said to be weak if its image under any conformal mapping of D consists of a single point. If γ is not weak, then we say that γ is unstable (Sario [3], [4]).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 17 , August 1960 , pp. 219 - 223
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1960

References

[1] Ahlfors, L. V. and Beurling, A., Conformal invariants and function-theoretic null-sets, Acta Math., 83 (1950), 101–129.Google Scholar
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[3] Sario, L., Stability problems on boundary components, Proc. Conference Analytic Function, Princeton (1957), 55–72.Google Scholar
[4] Sario, L., Strong and weak boundary components, Jour. Analyse Math., 5 (1958), 389–398.Google Scholar
[5] Savage, N., Weak boundary components of an open Riemann surface, Duke Math. Jour., 24 (1957), 79–95.CrossRefGoogle Scholar