Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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SOME APPLICATIONS OF EXTREMAL LENGTH TO CONFORMAL IMBEDDINGS

  • Chung, Bo-Hyun (Mathematics Section, College of Science and Technology Hongik University)
  • Received : 2009.03.17
  • Accepted : 2009.05.15
  • Published : 2009.06.30
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Abstract

Let G be a Denjoy domain and let G' a Denjoy proper subdomain of G and homeomorphic to G. We consider conformal re-imbeddings of G' into G. Let G and G' are N-connected. We know that if N = 2, there is a re-imbedding f of G' into G such that G - cl(f(G')) has an interior point. In this note, we obtain the following theorem. If $N{\geq}3$, G has a Denjoy proper subdomain G' such that, for any re-imbeddings f of G' into G, G - cl(f(G') has no interior point.

Keywords

Acknowledgement

Supported by : Korean Council for University Education

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