충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제22권2호
  • /
  • Pages.211-216
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  • 2009
  • /
  • 1226-3524(pISSN)
  • /
  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
권호 표지

SOME APPLICATIONS OF EXTREMAL LENGTH TO CONFORMAL IMBEDDINGS

  • Chung, Bo-Hyun (Mathematics Section, College of Science and Technology Hongik University)
  • 투고 : 2009.03.17
  • 심사 : 2009.05.15
  • 발행 : 2009.06.30
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초록

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.

키워드

과제정보

연구 과제 주관 기관 : Korean Council for University Education

참고문헌

  1. H. Ishida and F. Maitani, Conformal imbeddings of Denjoy domains II (in preparation).
  2. S. Nishimura and H. Ishida, Extremal length and the moduli space of triply connected plane regions, Acta Human. Sci. Univ. Sangio Kyotiensis, 25 (1995), 58-68.
  3. M. Ohtsuka, Dirichlet problem, extremal length and prime ends, Van Nostland, 1970.
  4. R. C. Penner, Extremal lengths on Denjoy domains, Proc. Amer. math. Soc. 102 (1988), 641-645. https://doi.org/10.1090/S0002-9939-1988-0928996-4
  5. L. Sario, and K. Oikawa, Capacity functions, Springer-Verlag, 1969.
  6. B. H. Chung, Some applications of extremal length to analytic functions, Commun. Korean Math. Soc. 21 (2006), no. 1, 135-143. https://doi.org/10.4134/CKMS.2006.21.1.135
  7. B. H. Chung, Extremal length and geometric inequalities, J. Chungcheong Math. Soc., 20 (2007), 147-156.
  8. B. H. Chung, and W. S. Jung, Some results related to Extremal length, J. Chungcheong Math. Soc. 16 (2003), 49-60.