Continuations of Riemann Surfaces
Canadian journal of mathematics, Tome 44 (1992) no. 2, pp. 357-367

Voir la notice de l'article provenant de la source Cambridge University Press

We shall show that if a Riemann surface is continuable, then it admits one of three types of continuations. Using this classification of continuations, we construct two nontrivial examples of two-sheeted unlimited covering Riemann surfaces of the unit disk one of which is continuable and the other is not.
DOI : 10.4153/CJM-1992-024-1
Mots-clés : Primary:, 30F20, secondary:, 30F15
Sakai, Makoto. Continuations of Riemann Surfaces. Canadian journal of mathematics, Tome 44 (1992) no. 2, pp. 357-367. doi: 10.4153/CJM-1992-024-1
@article{10_4153_CJM_1992_024_1,
     author = {Sakai, Makoto},
     title = {Continuations of {Riemann} {Surfaces}},
     journal = {Canadian journal of mathematics},
     pages = {357--367},
     year = {1992},
     volume = {44},
     number = {2},
     doi = {10.4153/CJM-1992-024-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1992-024-1/}
}
TY  - JOUR
AU  - Sakai, Makoto
TI  - Continuations of Riemann Surfaces
JO  - Canadian journal of mathematics
PY  - 1992
SP  - 357
EP  - 367
VL  - 44
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1992-024-1/
DO  - 10.4153/CJM-1992-024-1
ID  - 10_4153_CJM_1992_024_1
ER  - 
%0 Journal Article
%A Sakai, Makoto
%T Continuations of Riemann Surfaces
%J Canadian journal of mathematics
%D 1992
%P 357-367
%V 44
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1992-024-1/
%R 10.4153/CJM-1992-024-1
%F 10_4153_CJM_1992_024_1

[1] 1. Bochner, S., Fortsetzung Riemannscher Flächen, Math. Ann., 98(1928), 406–421. Google Scholar

[2] 2. Jurchescu, N., Bordered Riemann surfaces, Math. Ann., 143(1961), 264–292. Google Scholar

[3] 3. Lehto, O. and Virtanen, K.I., QuasiconformalMapping in the Plane, Sec. Ed. Springer-Verlag, Berlin, 1973. Google Scholar

[4] 4. Oikawa, K., Riemann Surfaces, to be translated from Japanese into English. Google Scholar

[5] 5. Radó, T., Über eine nicht fortsetzbare Riemannsche Mannigfaltigkeit, Math. Z., 20(1924), 1–6. Google Scholar

[6] 6. Renggli, H., Structural instability and extensions of Riemann surfaces, Duke Math. J., 42(1975), 211–224. Google Scholar

[7] 7. Sakai, M., On the vanishing of the span of a Riemann surface, Duke Math. J., 41(1974), 497–510. Google Scholar

[8] 8. Sario, L. and Oikawa, K., Capacity Functions, Springer-Verlag, Berlin, 1969. Google Scholar

[9] 9. Shiba, M., The Riemann-Hurwitz relation, parallel slit covering map, and continuation of an open Riemann surface of finite genus, Hiroshima Math. J., 14(1984), 371–399. Google Scholar

[10] 10. Tamura, J., On a theorem of T suji, Japan J. Math., 29(1959), 138–140.. Google Scholar

Cité par Sources :