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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
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  • 1. M. Glasner and R. Katz, On the behavior of solutions of ∆u = Pu at the Royden boundary, J. Analyse Math. 22 (1969), 345-354. MR 257344
  • 2. M. Glasner, R. Katz and M. Nakai, Examples in the classification theory of Riemannian manifolds and the equation ∆u = Pu, Math. Z. (to appear). MR 293536
  • 3. L. Myrberg, Über die Existenz der Greenschen Funktion der Gleichung ∆u = c(P)u auf Riemannschen Flächen, Ann. Acad. Sci. Fenn. Ser. A I Math.-Phys. No. 170 (1954). MR 16, 34. MR 62879
  • 4. M. Nakai, The space of bounded solutions of the equation ∆u = Pu on a Riemann surface, Proc. Japan Acad. 36 (1960), 267-272. MR 22 #12216. MR 121478
  • 5. M. Nakai, The space of Dirichlet-finite solutions of the equation ∆u = Pu on a Riemann surface, Nagoya Math. J. 18 (1961), 111-131. MR 23 #A1027. MR 123705
  • 6. M. Nakai, Dirichlet finite solutions of ∆u = Pu, and classification of Riemann surfaces, Bull. Amer. Math. Soc. 77 (1971), 381-385. MR 293083
  • 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 $E\sp m$ with almost rotation free $P \geq O$, Tõhoku Math. J. (to appear).
  • 9. M. Ozawa, Classification of Riemann surfaces, Kõdai Math. Sem. Rep. 1952, 63-76. MR 14, 462. MR 51322
  • 10. H. Royden, The equation ∆u = Pu, and the classification of open Riemann surfaces, Ann. Acad. Sci. Fenn. Ser. A. I. No. 271 (1959). MR 22 #12215. MR 121477
  • 11. L. Sario and M. Nakai, Classification theory of Riemann surfaces, Springer-Verlag, Berlin, 1970. MR 264064

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DOI: https://doi.org/10.1090/S0002-9904-1971-12725-8

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