A remark on classification of Riemannian manifolds with respect to Δ𝑢=𝑃𝑢

Glasner, Moses; Katz, Richard; Nakai, Mitsuru

doi:10.1090/S0002-9904-1971-12725-8

A remark on classification of Riemannian manifolds with respect to $\Delta u = Pu$
HTML articles powered by AMS MathViewer

by Moses Glasner, Richard Katz and Mitsuru Nakai PDF

Bull. Amer. Math. Soc. 77 (1971), 425-428

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
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), 233–238. MR 293536, DOI 10.1007/BF01111596
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 bounded solutions of the equation $\Delta u=pu$ on a Riemann surface, Proc. Japan Acad. 36 (1960), 267–272. 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), 111–131. MR 123705, DOI 10.1017/S0027763000002270
Mitsuru Nakai, Dirichlet finite solutions of $\Delta u=Pu$, and classification of Riemann surfaces, Bull. Amer. Math. Soc. 77 (1971), 381–385. MR 293083, DOI 10.1090/S0002-9904-1971-12705-2
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, 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