Author:
Akaza Tohru,Oikawa Kôtaro
Abstract
Let D be a plane domain and Γ be a component of the boundary of D consisting of a single point. According to Sario [5] we shall call Γ a weak boundary component of D if its image under any conformal mapping of D consists of a single point. A weak boundary component has been introduced by Grötzsch [2], who called it “vollkommen punktförmig”. If Γ is not weak we shall say that it is unstable (Sario [5]). We know that the weakness depends merely on the configuration of D in a neighborhood of Γ (see [4], p. 274).
Publisher
Cambridge University Press (CUP)
Reference5 articles.
1. Eine Bemerkung zum Koebeschen Kreisnormierungsprinzip;Grötzsch;Ber. Verh. Sachs. Akad. Wiss. Leipzig. Math.-Nat. Kl.,1935
2. On the stability of boundary components;Oikawa;Ibid.,1960
3. Modulus of a boundary component
4. On the Weakness of Some Boundary Component
5. Strong and weak boundary components
Cited by
2 articles.
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1. The method of extremal length;Bulletin of the American Mathematical Society;1974
2. On weak and unstable components;Hiroshima Mathematical Journal;1964-01-01