Abstract
The purpose of this work is to obtain a new type of conformal mappings of compact finite Riemann surfaces bounded by finitely many analytic Jordan curves. This is achieved by making use of Riemann-Roch theorem. As is well-known, every plane region is conformally equivalent to a parallel slit region. This theorem was carried over the case of Riemann surfaces with finite genus. The other types of conformal mappings can be found in the different literatures. It will be now deal with a different conformal mapping from those. It is a finite sheeted covering surface of the extended complex plane whose each boundary component consists of a closed interval on real axis.
Keywords
Riemann Surfaces Conformal Mapping Jordan Curves Riemann-Roch Theorem Meromorphic Function.
References
- • Shiba, M., (1971). “On the Riemann-Roch Theorem on Open Riemann Surface”, J. Of Math. Of Kyoto Univ., vol. 11(3), pp.495-525.
- • Shiba, M., (1975). “Notes on Existence of Certain Slit Mappings”, Proc. of the Japan Academy, vol. 51(8), pp. 687-690.
- • Ahlfors, L.V., and Sario, L., (1960). “Riemann Surfaces” Princeton Univ. Pres.
- • Başkan, T., (1976). “On some behavior spaces and Riemann- Roch theorem on Open Riemann Surfaces”, J. Math. Kyoto Univ., vol. 16, pp. 101-112.
- • Başkan, T., (1981). “On a generalization of behavior spaces and Riemann- Roch theorem on Open Riemann Surfaces”, Ibid, vol 21 (2), pp. 319-329.
- • Matsui, K., (1977). “Convergence Theorems of Abelian Differentials with Applications to Conformal Mappings II”, J. Math. Kyoto Univ., vol. 17 (2), pp. 345-373.
- • Kusunoki, Y., (1959). “Contributions to Riemann- Roch’s Theorem”, Mem. Col.svi. Univ. Kyotoser. A. Math., vol. 32, pp. 235-258.
Abstract
Bu çalışmanın amacı, sonlu sayıda analitik Jordan eğrileri ile sınırlanan kompakt sonlu Riemann yüzeylerinin konformal dönüşümlerinin yeni bir tipini elde etmektir. Bu, yararlanılarak elde edilir. Bilindiği üzere, her bir düzlem bölgesi konformal olarak paralel bir yarık bölgeye eşdeğerdir. Bu teorem cinsi sonlu Riemann yüzeylerine uygulanmıştır. Konformal dönüşümlerin diğer tipleri farklı eserlerde incelenmiştir. Burada farklı bir konformal dönüşümle ilgilenilecektir. Her sınır bileşeni gerçel eksen üzerinde ve kapalı bir aralık genişletilmiş kompleks düzlemin sonlu örtüsüdür
Keywords
References
- • Shiba, M., (1971). “On the Riemann-Roch Theorem on Open Riemann Surface”, J. Of Math. Of Kyoto Univ., vol. 11(3), pp.495-525.
- • Shiba, M., (1975). “Notes on Existence of Certain Slit Mappings”, Proc. of the Japan Academy, vol. 51(8), pp. 687-690.
- • Ahlfors, L.V., and Sario, L., (1960). “Riemann Surfaces” Princeton Univ. Pres.
- • Başkan, T., (1976). “On some behavior spaces and Riemann- Roch theorem on Open Riemann Surfaces”, J. Math. Kyoto Univ., vol. 16, pp. 101-112.
- • Başkan, T., (1981). “On a generalization of behavior spaces and Riemann- Roch theorem on Open Riemann Surfaces”, Ibid, vol 21 (2), pp. 319-329.
- • Matsui, K., (1977). “Convergence Theorems of Abelian Differentials with Applications to Conformal Mappings II”, J. Math. Kyoto Univ., vol. 17 (2), pp. 345-373.
- • Kusunoki, Y., (1959). “Contributions to Riemann- Roch’s Theorem”, Mem. Col.svi. Univ. Kyotoser. A. Math., vol. 32, pp. 235-258.
Details
| Primary Language | English |
|---|---|
| Journal Section | Chemistry |
| Authors | |
| Publication Date | April 7, 2015 |
| Published in Issue | Year 2015 |