Dirichlet finite solutions of $\Delta u = Pu$, and classification of Riemann surfaces
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- by Mitsuru Nakai PDF
- Bull. Amer. Math. Soc. 77 (1971), 381-385
References
- Moses Glasner and Richard Katz, On the behavior of solutions of $\Delta u=Pu$ at the Royden boundary, J. Analyse Math. 22 (1969), 343–354. MR 257344, DOI 10.1007/BF02786798
- Lauri Myrberg, Über die Existenz der Greenschen Funktion der Gleichung $\Delta u=c(P)\cdot u$ auf Riemannschen Flächen, Ann. Acad. Sci. Fennicae Ser. A. I. Math.-Phys. 1954 (1954), no. 170, 8 (German). MR 62879
- Mitsuru Nakai, The space of Dirichlet-finite solutions of the equation $\Delta u=Pu$ on a Riemann surface, Nagoya Math. J. 18 (1961), 111–131. MR 123705, DOI 10.1017/S0027763000002270
- Mitsuru Ozawa, Classification of Riemann surfaces, K\B{o}dai Math. Sem. Rep. 4 (1952), 63–76. {Volume numbers not printed on issues until Vol. 7 (1955)}. MR 51322
- H. L. Royden, Harmonic functions on open Riemann surfaces, Trans. Amer. Math. Soc. 73 (1952), 40–94. MR 49396, DOI 10.1090/S0002-9947-1952-0049396-8
- H. L. Royden, The equation $\Delta u=Pu$, and the classification of open Riemann sufaces, Ann. Acad. Sci. Fenn. Ser. A I No. 271 (1959), 27. MR 0121477
- L. Sario and M. Nakai, Classification theory of Riemann surfaces, Die Grundlehren der mathematischen Wissenschaften, Band 164, Springer-Verlag, New York-Berlin, 1970. MR 0264064, DOI 10.1007/978-3-642-48269-4
- K. I. Virtanen, Über die Existenz von beschränkten harmonischen Funktionen auf offenen Riemannschen Flächen, Ann. Acad. Sci. Fennicae Ser. A. I. Math.-Phys. 1950 (1950), no. 75, 8 (German). MR 38443
Additional Information
- Journal: Bull. Amer. Math. Soc. 77 (1971), 381-385
- MSC (1970): Primary 30A48, 31B05, 35J05, 53C20
- DOI: https://doi.org/10.1090/S0002-9904-1971-12705-2
- MathSciNet review: 0293083