Acta Mathematica

Lp and mean value properties of subharmonic functions on Riemannian manifolds

Peter Li and Richard Schoen

Full-text: Open access


Research supported in part by a Sloan Fellowship and an NSF grant, MCS81-07911.


Research supported in part by an NSF grant, MCS-80-23356.

Article information

Acta Math. Volume 153 (1984), 279-301.

Received: 23 August 1983
Revised: 8 December 1983
First available in Project Euclid: 31 January 2017

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

1984 © Almqvist & Wiksell


Li, Peter; Schoen, Richard. L p and mean value properties of subharmonic functions on Riemannian manifolds. Acta Math. 153 (1984), 279--301. doi:10.1007/BF02392380.

Export citation


  • Anderson, M., The Dirichlet problem at infinity for manifolds of negative curvature. To appear in J. Differential Geom.
  • Anderson, M. & Schoen, R., Preprint.
  • 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.
  • Cheng, S. Y. & Yau, S. T., Differential equations on Riemannian manifolds and their geometric applications. Comm. Pure Appl. Math., 28 (1975), 333–354.
  • Chung, L. O., Existence of harmonic L1 functions in complete Riemannian manifolds. Unpublished.
  • Garnett, L., Foliations, the ergodic theorem and brownian motion. Preprint.
  • Greene, R. E. & Wu, H., Integrals of subharmonic functions on manifolds of nonnegative curvature. Invent. Math., 27 (1974), 265–298.
  • —, Function theory on manifolds which possess a pole. Lecture Notes in Mathematics, 699. Springer-Verlag, Berlin-Heidelberg-New York (1979).
  • Karp, L. & Li, P., The heat equation on complete Riemannian manifolds. Preprint.
  • Li, P. & Yau, S. T., Estimates of eigenvalues of a compact Riemannian manifold. Proc. Symp. Pure Math., 36 (1980), 205–239.
  • Strichartz, R., Analysis of the Laplacian on a complete Riemannian manifold. J. Funct. Anal., 52 (1983), 48–79.
  • Sullivan, D., Preprint.
  • Wu, H., On the volume of a noncompact manifold. Duke Math. J., 49 (1982), 71–78.
  • Yau, S. T., Harmonic functions on complete Riemannian manifolds. Comm. Pure Appl. Math., 28 (1975), 201–228.
  • —, Some function-theoretic properties of complete Riemannian manifolds and their applications to geometry. Indiana Univ. Math. J., 25 (1976), 659–670.