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CONFORMAL MAPPINGS OF FINITE RIEMANN SURFACES

Year 2015, , 21 - 28, 07.04.2015

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.

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.

SONLU RIEMANN YÜZEYLERİNİN KONFORMAL DÖNÜŞÜMLERİ

Year 2015, , 21 - 28, 07.04.2015

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

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.
There are 7 citations in total.

Details

Primary Language English
Journal Section Chemistry
Authors

Güner Ilıcan

Publication Date April 7, 2015
Published in Issue Year 2015

Cite

APA Ilıcan, G. (2015). CONFORMAL MAPPINGS OF FINITE RIEMANN SURFACES. Physical Sciences21-28. https://doi.org/10.12739/NWSA.2015.10.2.3A0069
AMA Ilıcan G. CONFORMAL MAPPINGS OF FINITE RIEMANN SURFACES. Physical Sciences. Published online April 1, 2015:21-28. doi:10.12739/NWSA.2015.10.2.3A0069
Chicago Ilıcan, Güner. “CONFORMAL MAPPINGS OF FINITE RIEMANN SURFACES”. Physical Sciences, April (April 2015), 21-28. https://doi.org/10.12739/NWSA.2015.10.2.3A0069.
EndNote Ilıcan G (April 1, 2015) CONFORMAL MAPPINGS OF FINITE RIEMANN SURFACES. Physical Sciences 21–28.
IEEE G. Ilıcan, “CONFORMAL MAPPINGS OF FINITE RIEMANN SURFACES”, Physical Sciences, pp. 21–28, April 2015, doi: 10.12739/NWSA.2015.10.2.3A0069.
ISNAD Ilıcan, Güner. “CONFORMAL MAPPINGS OF FINITE RIEMANN SURFACES”. Physical Sciences. April 2015. 21-28. https://doi.org/10.12739/NWSA.2015.10.2.3A0069.
JAMA Ilıcan G. CONFORMAL MAPPINGS OF FINITE RIEMANN SURFACES. Physical Sciences. 2015;:21–28.
MLA Ilıcan, Güner. “CONFORMAL MAPPINGS OF FINITE RIEMANN SURFACES”. Physical Sciences, 2015, pp. 21-28, doi:10.12739/NWSA.2015.10.2.3A0069.
Vancouver Ilıcan G. CONFORMAL MAPPINGS OF FINITE RIEMANN SURFACES. Physical Sciences. 2015:21-8.