Bounded harmonic maps on a class of manifolds
Authors:
ChiungJue Sung, Luenfai Tam and Jiaping Wang
Journal:
Proc. Amer. Math. Soc. 124 (1996), 22412248
MSC (1991):
Primary 58E20
MathSciNet review:
1307567
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Abstract 
References 
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Additional Information
Abstract: Without imposing any curvature assumptions, we show that bounded harmonic maps with image contained in a regular geodesic ball share similar behaviour at infinity with the bounded harmonic functions on the domain manifold.
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 M. Cai, Ends of Riemannian manifolds with nonnegative Ricci curvature outside a compact set, Bull. AMS 24 (1991), 371377. MR 92f:53045
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 S. Y. Cheng and S. T. Yau, Differential equations on Riemannian manifolds and their geometric applications, Comm. Pure Appl. Math. 28 (1975), 333354. MR 52:6608
 [Ch]
 H. I. Choi,, On the Liouville theorem for harmonic maps, Proc. AMS 85 (1982), 9194. MR 83j:53073
 [Go]
 W. B. Gordon, Convex functions and harmonic maps, Proc. AMS 33 (1972), 433437. MR 45:1075
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 [HKW]
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 W. S. Kendall,, Probability, convexity, and harmonic maps with small image I: uniqueness and fine existence, Proc. London Math. Soc. 61 (3) (1990), 371406. MR 91g:58062
 [LT 1]
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 [LT 2]
 P. Li and L. F. Tam, Symmetric Green's functions on complete manifolds, Amer. J. Math. 109 (1987), 11291154. MR 89f:58129
 [LT 3]
 P. Li and L. F. Tam, Complete surfaces with finite total curvature, J. Diff. Geom. 33 (1991), 139168. MR 92e:53051
 [LT 4]
 P. Li and L. F. Tam, Harmonic functions and the structure of complete manifolds, J. Diff. Geom. 35 (1992), 359383. MR 93b:53033
 [LT 5]
 P. Li and L. F. Tam, Green's Functions, Harmonic Functions and Volume Comparison, J. Diff. Geom., vol. 41, 1995, pp. 277318.
 [Liu]
 ZD. Liu, Ball covering on manifolds with nonnegative Ricci curvature near infinity, preprint.
 [S]
 C. J. Sung, Harmonic functions under quasiisometry, to appear in J. Geom. Anal..
 [Y]
 S. T. Yau, Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math. 28 (1975), 201228. MR 55:4042
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Additional Information
ChiungJue Sung
Affiliation:
Department of Mathematics, National Chung Cheng University, ChiaYi, Taiwan 62117
Email:
cjsung@math.ccu.edu.tw
Luenfai Tam
Affiliation:
Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong
Email:
lftam@math.cuhk.hk
Jiaping Wang
Affiliation:
Department of Mathematics, Stanford University, Stanford, California 94305
Email:
jwang@math.stanford.edu
DOI:
http://dx.doi.org/10.1090/S0002993996032467
PII:
S 00029939(96)032467
Received by editor(s):
December 16, 1994
Additional Notes:
The first author was partially supported by NSC grant# 830208M194030.
The second author was partially supported by NSF grant #DMS9300422 .
Communicated by:
Peter Li
Article copyright:
© Copyright 1996
American Mathematical Society
