Acta Mathematica

, Volume 153, Issue 1, pp 279–301 | Cite as

L p and mean value properties of subharmonic functions on Riemannian manifolds

  • Peter Li
  • Richard Schoen
Article

Keywords

Manifold Riemannian Manifold Subharmonic Function 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Anderson, M., The Dirichlet problem at infinity for manifolds of negative curvature. To appear inJ. Differential Geom.Google Scholar
  2. [2]
    Anderson, M. & Schoen, R., Preprint.Google Scholar
  3. [3]
    Cheeger, J., Gromov, M. &Taylor, M., Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds.J. Differential Geom., 17 (1983), 15–53.MathSciNetGoogle Scholar
  4. [4]
    Cheng, S. Y. &Yau, S. T., Differential equations on Riemannian manifolds and their geometric applications.Comm. Pure Appl. Math., 28 (1975), 333–354.MathSciNetGoogle Scholar
  5. [5]
    Chung, L. O., Existence of harmonicL 1 functions in complete Riemannian manifolds. Unpublished.Google Scholar
  6. [6]
    Garnett, L., Foliations, the ergodic theorem and brownian motion. Preprint.Google Scholar
  7. [7]
    Greene, R. E. &Wu, H., Integrals of subharmonic functions on manifolds of nonnegative curvature.Invent. Math., 27 (1974), 265–298.CrossRefMathSciNetGoogle Scholar
  8. [8]
    —,Function theory on manifolds which possess a pole. Lecture Notes in Mathematics, 699. Springer-Verlag, Berlin-Heidelberg-New York (1979).Google Scholar
  9. [9]
    Karp, L. & Li, P., The heat equation on complete Riemannian manifolds. Preprint.Google Scholar
  10. [10]
    Li, P. &Yau, S. T., Estimates of eigenvalues of a compact Riemannian manifold.Proc. Symp. Pure Math., 36 (1980), 205–239.MathSciNetGoogle Scholar
  11. [11]
    Strichartz, R., Analysis of the Laplacian on a complete Riemannian manifold.J. Funct. Anal., 52 (1983), 48–79.CrossRefMATHMathSciNetGoogle Scholar
  12. [12]
    Sullivan, D., Preprint.Google Scholar
  13. [13]
    Wu, H., On the volume of a noncompact manifold.Duke Math. J., 49 (1982), 71–78.CrossRefMATHMathSciNetGoogle Scholar
  14. [14]
    Yau, S. T., Harmonic functions on complete Riemannian manifolds.Comm. Pure Appl. Math., 28 (1975), 201–228.MATHMathSciNetGoogle Scholar
  15. [15]
    —, Some function-theoretic properties of complete Riemannian manifolds and their applications to geometry.Indiana Univ. Math. J., 25 (1976), 659–670.CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Almqvist & Wiksell 1984

Authors and Affiliations

  • Peter Li
    • 1
  • Richard Schoen
    • 2
  1. 1.Purdue UniversityWest LafayetteUSA
  2. 2.University of CaliforniaBerkeleyUSA

Personalised recommendations