A remark on classification of Riemannian manifolds with respect to $\Delta u = Pu$
Authors:
Moses Glasner, Richard Katz and Mitsuru Nakai
Journal:
Bull. Amer. Math. Soc. 77 (1971), 425-428
MSC (1970):
Primary 30A48, 31B05, 35J05, 53C20
DOI:
https://doi.org/10.1090/S0002-9904-1971-12725-8
MathSciNet review:
0276897
Full-text PDF Free Access
References | Similar Articles | Additional Information
- Moses Glasner and Richard Katz, On the behavior of solutions of $\Delta u=Pu$ at the Royden boundary, J. Analyse Math. 22 (1969), 343β354. MR 257344, DOI https://doi.org/10.1007/BF02786798
- Moses Glasner, Richard Katz, and Mitsuru Nakai, Examples in the classification theory of Riemannian manifolds and the equation $\triangle u=Pu$, Math. Z. 121 (1971), 233β238. MR 293536, DOI https://doi.org/10.1007/BF01111596
- Lauri Myrberg, Γber die Existenz der Greenschen Funktion der Gleichung $\Delta u=c(P)\cdot u$ auf Riemannschen FlΓ€chen, Ann. Acad. Sci. Fennicae Ser. A. I. Math.-Phys. 1954 (1954), no. 170, 8 (German). MR 62879
- Mitsuru Nakai, The space of bounded solutions of the equation $\Delta u=pu$ on a Riemann surface, Proc. Japan Acad. 36 (1960), 267β272. MR 121478
- Mitsuru Nakai, The space of Dirichlet-finite solutions of the equation $\Delta u=Pu$ on a Riemann surface, Nagoya Math. J. 18 (1961), 111β131. MR 123705
- Mitsuru Nakai, Dirichlet finite solutions of $\Delta u=Pu$, and classification of Riemann surfaces, Bull. Amer. Math. Soc. 77 (1971), 381β385. MR 293083, DOI https://doi.org/10.1090/S0002-9904-1971-12705-2 7. M. Nakai, Dirichlet finite solutions of ∆u = Pu on open Riemann surfaces, Kõdai Math. Sem. Rep. (to appear). 8. M. Nakai, The equation $\Deltau = Pu$ on $E^ m$ with almost rotation free $P \geq O$, Tõhoku Math. J. (to appear).
- Mitsuru Ozawa, Classification of Riemann surfaces, K\B{o}dai Math. Sem. Rep. 4 (1952), 63β76. {Volume numbers not printed on issues until Vol. 7 (1955)}. MR 51322
- 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
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