Advertisement

Results in Mathematics

, Volume 15, Issue 1–2, pp 81–103 | Cite as

Warped products with discrete spectra

  • Regina Kleine
Article

Keywords

Riemannian Manifold Sectional Curvature Ricci Curvature Isoperimetric Inequality Warped Product 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Baider, A.: Noncompact Riemannian Manifolds with discrete spectra. J. Differ. Geom. 14 (1979), 41–57MathSciNetMATHGoogle Scholar
  2. 2.
    Besse, A.L.: Einstein Manifolds. Berlin, Heidelberg, New York: Springer 1987MATHGoogle Scholar
  3. 3.
    Brüning, J.: On Schrödinger Operators with discrete spectrum. Preprint, Augsburg 1987Google Scholar
  4. 4.
    Buser, P.: A note on the isoperimetric constant. Ann. scient. Éc. Norm. Sup. 4e série, t. 15 (1982), 213–230MathSciNetMATHGoogle Scholar
  5. 5.
    Chavel, I.: Eigenvalues in Riemannian Geometry. Academic Press 1984Google Scholar
  6. 6.
    Croke, C.: Some isoperimetric inequalities and eigenvalue estimates. Ann. scient Éc. Norm. Sup. 4e série, t. 13 (1980), 419–435MathSciNetMATHGoogle Scholar
  7. 7.
    Donnelly, H., Li, P.: Pure point spectrum and negative curvature for noncompact manifolds. Duke Math. J. 46 (1979), 497–503MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Gray, A.: The volume of a small geodesic ball of a Riemannian manifold. Michigan Math. J. 20 (1973), 329–344MathSciNetMATHGoogle Scholar
  9. 9.
    Hildebrandt, S.: Harmonic mappings of Riemannian manifolds. Lecture Notes in Mathematics 1161: Harmonic Mappings and Minimal Immersions, Montecatini 1984. Springer 1985Google Scholar
  10. 10.
    Kanai, M.: Analytic inequalities and rough isometries between non-compact Riemannian manifolds. Lecture Notes in Mathematics 1201: Curvature and Topology, Proc. Katata 1985. Springer 1986Google Scholar
  11. 11.
    Kanai, M.: Rough isometries, and combinatorial approximations of noncompact Riemannian manifolds. J. Math. Soc. Japan 37 (1985), 391–413MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Kleine, R.: Discreteness conditions for the Laplacian on complete, noncompact Riemannian manifolds. Math. Z., 148 (1988), 127–141MathSciNetCrossRefGoogle Scholar
  13. 13.
    Li, P.: On the Sobolev constant and the p-spectrum of a compact Riemannian manifold. Ann. scient. Ec. Norm. Sup. 4e série, t 13 (1980), 451–469MATHGoogle Scholar
  14. 14.
    Maz’ya, V.G.: On (p, L)-capacity, imbedding theorems, and the spectrum of a selfadjoint elliptic operator. Math. USSR Izvestija 7 (1973), 357–387CrossRefGoogle Scholar
  15. 15.
    Maz’ya, V.G.: On removable singularities of bounded solutions of quasilinear elliptic equations of any order. J. Soviet Math. (1975), 480–492Google Scholar
  16. 16.
    Müller-Pfeiffer, E.: Über die Lokalisierung des wesentlichen Spektrums des Schrödingeroperators. Math. Nachr. 46 (1970), 157–170MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Yau, S.T.: Isoperimetric constants and the first eigenvalue of a compact Riemannian manifold. Ann. scient. Éc. Norm. Sup. 4e série, t. 8 (1975), 487–507MATHGoogle Scholar

Copyright information

© Birkhäuser Verlag, Basel 1989

Authors and Affiliations

  • Regina Kleine
    • 1
  1. 1.Regina Kleine Ruhr-Universität BochumBochum

Personalised recommendations