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Fundamental regions and the type problem for a Riemann surface. (English) Zbl 0423.30038


MSC:

30F20 Classification theory of Riemann surfaces
30F35 Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization)
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References:

[1] Ahlfors, L.V., Sario, L.: Riemann Surfaces. Princeton: Princeton University Press 1968 · Zbl 0196.33801
[2] Hopf, E.: Statistik der geodätischen Linien in Mannigfaltigkeiten negativer Krümmung. Ber. Verh. Sächs. Akad. Wiss. Leipzig91, 261-304 (1939) · JFM 65.1413.02
[3] Laasonen, P.: Zum Typenproblem der Riemannschen Flächen. Ann. Acad. Sci. Fenn. Ser. A.I.11 (1942) · JFM 68.0168.03
[4] Myrberg, P.J.: Sur la determination du type d’une surface Riemannienne simplement connexe. C.R. Acad. Sci. Paris200, 1818-1820 (1935) · Zbl 0011.31303
[5] Myrberg, P.J.: Über die Bestimmung des Typus einer Riemannschen Fläche. Ann. Acad. Sci. Fenn. Ser. A.I.45 (1935) · Zbl 0013.12203
[6] Pommerenke, Ch.: On the Green’s function of Fuchsian groups. Ann. Acad. Sci. Fenn. Ser. A.I.2, 409-427 (1976) · Zbl 0363.30029
[7] Purzitsky, N.: A cutting and pasting of non compact polygons with applications to Fuchsian groups. Acta Math.143, 233-250 (1979) · Zbl 0427.30039
[8] Purzitsky, N.: Fricke polygons for infinitely generated Fuchsian groups I. Preprint · Zbl 0427.30039
[9] Sario, L., Nakai, M.: Classification theory of Riemann Surfaces. Berlin-Heidelberg-New York: Springer 1970 · Zbl 0199.40603
[10] Tsuji, M.: Potential theory in modern function theory. Tokyo: Maruzen 1959 · Zbl 0087.28401
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