Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M.T. Anderson: The Dirichlet problem at infinity for manifolds with negative curvaturte, J. Diff. Geom. 18 (1983), 701–721.
M.T. Anderson and R. Schoen: Positive harmonic functions on complete manifolds of negative curvature, Ann. of Math. 121 (1985), 429–461.
S.-Y. Cheng: Liouville theorems for harmonic maps, Proc. Symp. Pure Math. 36, A.M.S. 1980, 147–151.
S.-Y. Cheng and S.T. Yau: Differential equations on Riemannian and their geometric applications, Comm. Pure Appl. Math. 28 (1975), 333–354.
H. Donnelly: Bounded harmonic functions and positive Ricci curvature Math. Z. 191 (1986), 559–565.
M. Finn: On a class of comformal metrics, with applications to differential geometry in the large, Comm. Math. He; v. 40 (1965), 1–30.
R.E. Greene and H. Wu: Embedding of open Riemannian manifolds by harmonic functions, Ann. Inst. Fourier (Grenoble) 25 (1975), 215–235.
A. Kasue: On manifolds of asymptotically nonnegative curvature, M.S.R.I. Berkeley, Calf. Preprint #09208-86, July, 1986 (unpublished)
—: A compactification of a manifold with asymptotically nonnegative curvature, to appear.
—: A convergence theorem for Riemannian manifolds and some applications, to appear.
J.L. Kazdan: Parabolicity and the Liouville property on complete Riemannian manifolds, Seminar on New Results in Nonlinear Partial Differential Equations, A Publication of the Max-Plank-Inst. für Math. (1987), 153–166, Bonn.
P. Li and L.-F. Tam: Positive harmonic functions on complete manifolds with non-negative curvature outside a compact set, Ann. of Math. 125 (1987), 171–207.
—: Symmetric Green's functions on complete manifolds, to appear in Amer. J. Math.
D. Sullivan: The Diricjlet problem at infinity for a negatively curved manifold, J. Diff. Geom. 18 (1983), 723–732.
H. Wu: The Bochner Technique in Differential Geometry, to appear.
—: Some open problems in the study of noncompact Kähler manifolds, Lecture presented at the Kyoto Conference on Geometric Function Theory, Sep. 8, 1978.
S.-T. Yau: Harminic functions on complete Riemannian manifolds, Comm. Pure Appl. Math. 28 (1975), 201–228.
Editor information
Rights and permissions
Copyright information
© 1988 Springer-Verlag
About this paper
Cite this paper
Kasue, A. (1988). Harmonic functions with growth conditions on a manifold of asymptotically nonnegative curvature I. In: Sunada, T. (eds) Geometry and Analysis on Manifolds. Lecture Notes in Mathematics, vol 1339. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083054
Download citation
DOI: https://doi.org/10.1007/BFb0083054
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50113-8
Online ISBN: 978-3-540-45930-9
eBook Packages: Springer Book Archive