Bounded harmonic maps on a class of manifolds

Proceedings of the American Mathematical Society

Volumn 124, Issue 7, 1996, Pages 2241-2248

  Sung, Chiung Jue ^a   Tam, Luen Fai ^b   Wang, Jiaping ^c  

^a NATIONAL CHUNG CHENG UNIVERSITY   (Taiwan)

^b CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

^c STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21344465089     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9939-96-03246-7     Document Type: Article

References (21)

1. [A-C-M] P. Avilés, H.I. Choi, and M. Micallef, Boundary behavior of harmonic maps on nonsmooth domains and complete negatively curved manifolds, J. Functional Anal. 99 (1991), 293-331. MR 92j:58025
2. [Cai] M. Cai, Ends of Riemannian manifolds with nonnegative Ricci curvature outside a compact set, Bull. AMS 24 (1991), 371-377. MR 92f:53045
3. [C-G 2] J. Cheeger and D. Gromoll, On the structure of complete manifolds of nonnegative curvature, Ann. of Math. 92 (1972), 413-443. MR 46:8121
4. [Cg] S. Y. Cheng, Liouville Theorem for Harmonic Maps, Proc. of Symposia in Pure Math. 36 (1980), 147-151. MR 81i:58021
5. [C-Y] S. Y. Cheng and S. T. Yau, Differential equations on Riemannian manifolds and their geometric applications, Comm. Pure Appl. Math. 28 (1975), 333-354. MR 52:6608
6. [Ch] H. I. Choi, On the Liouville theorem for harmonic maps, Proc. AMS 85 (1982), 91-94. MR 83j:53073
7. [Go] W. B. Gordon, Convex functions and harmonic maps, Proc. AMS 33 (1972), 433-437. MR 45:1075
8. [G-W] R. E. Green and H. Wu, Function theory on Manifolds which possess a pole, Lecture Notes in Math. 699 (1979), Springer-Verlag.
9. [H-K-W] S. Hildebrandt, H. Kaul and K.-O. Widman, An existence theory for harmonic mappings of Riemannian manifolds, Acta Math. 138 (1977), 1-16. MR 55:6478
10. [J-K] Jäger, W. and Kaul, H., Uniqueness and stability of harmonic maps and their Jocobi fields, Manu. Math. 28 (1979), 269-291. MR 80j:58030
11. [K 1] A. Kasue, A compactification of a manifold with asymptotically nonnegative curvature, Ann. Scient. Ec. Norm. Sup. 21 (1988), 593-622. MR 90d:53049
12. [K 2] A. Kasue, Harmonic functions with growth conditions on a manifold of asymptotically nonnegative curvature I, Geometry and Analysis on Manifolds (1988), Springer-Verlag Lecture Notes in Mathematics 1339, 158-181. MR 89i:53030
13. [Ke] W. S. Kendall, Probability, convexity, and harmonic maps with small image I: uniqueness and fine existence, Proc. London Math. Soc. 61 (3) (1990), 371-406. MR 91g:58062
14. [L-T 1] P. Li and L. F. Tam, Positive harmonic functions on complete manifolds with nonnegative curvature outside a compact set., Annals Math. 125 (1987), 171-207. MR 88m:58039
15. [L-T 2] P. Li and L. F. Tam, Symmetric Green's functions on complete manifolds, Amer. J. Math. 109 (1987), 1129-1154. MR 89f:58129
16. [L-T 3] P. Li and L. F. Tam, Complete surfaces with finite total curvature, J. Diff. Geom. 33 (1991), 139-168. MR 92e:53051
17. [L-T 4] P. Li and L. F. Tam, Harmonic functions and the structure of complete manifolds, J. Diff. Geom. 35 (1992), 359-383. MR 93b:53033
18. [L-T 5] P. Li and L. F. Tam, Green's Functions, Harmonic Functions and Volume Comparison, J. Diff. Geom. 41 (1995), 277-318.
19. [Liu] Z-D. Liu, Ball covering on manifolds with nonnegative Ricci curvature near infinity, preprint.
20. [S] C. J. Sung, Harmonic functions under quasi-isometry, to appear in J. Geom. Anal..
21. [Y] S. T. Yau, Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math. 28 (1975), 201-228. MR 55:4042