Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-24T03:59:33.923Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
[2] Oikawa, K., On the stability of boundary component, Pacific Jour. Math., 10 (1960), 263–294.CrossRefGoogle Scholar
[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