학술저널
SOME APPLICATIONS OF EXTREMAL LENGTH TO CONFORMAL IMBEDDINGS
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 22, No. 2
-
2009.06211 - 216 (6 pages)
- 0
Let G be a Denjoy domain and let G0 a Denjoy proper subdomain of G and homeomorphic to G. We consider conformal re-imbeddings of G0 into G. Let G and G0 are N-connected. We know that if N = 2, there is a re-imbedding f of G0 into G such that G ¡ cl(f(G0)) has an interior point. In this note, we obtain the following theorem. If N ¸ 3, G has a Denjoy proper subdomain G0 such that, for any re-imbeddings f of G0 into G, G ¡ cl(f(G0)) has no interior point.
1. Introduction
2. Extremal length
3. Extremal length and conformal imbeddings
References
(0)
(0)