Bulletin of the American Mathematical Society

A remark on classification of Riemannian manifolds with respect to $\Delta u = Pu$

Moses Glasner, Richard Katz, and Mitsuru Nakai

Full-text: Open access

Article information

Source
Bull. Amer. Math. Soc., Volume 77, Number 3 (1971), 425-428.

Dates
First available in Project Euclid: 4 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.bams/1183532825

Mathematical Reviews number (MathSciNet)
MR0276897

Zentralblatt MATH identifier
0212.45003

Subjects
Primary: 30A48 31B05: Harmonic, subharmonic, superharmonic functions 35J05: Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation [See also 31Axx, 31Bxx] 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]

Citation

Glasner, Moses; Katz, Richard; Nakai, Mitsuru. A remark on classification of Riemannian manifolds with respect to $\Delta u = Pu$. Bull. Amer. Math. Soc. 77 (1971), no. 3, 425--428. https://projecteuclid.org/euclid.bams/1183532825


Export citation

References

  • 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.
  • 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).
  • 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.
  • 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.
  • 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.
  • 6. M. Nakai, Dirichlet finite solutions of ∆u = Pu, and classification of Riemann surfaces, Bull. Amer. Math. Soc. 77 (1971), 381-385.
  • 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.
  • 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.
  • 11. L. Sario and M. Nakai, Classification theory of Riemann surfaces, Springer-Verlag, Berlin, 1970.