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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