On the Liouville theorem for harmonic maps
Author:
Hyeong In Choi
Journal:
Proc. Amer. Math. Soc. 85 (1982), 9194
MSC:
Primary 53C99; Secondary 58E20
MathSciNet review:
647905
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Abstract: Suppose and are complete Riemannian manifolds; with Ricci curvature bounded below by , , with sectional curvature bounded above by a positive constant . Let be a harmonic map such that . If lies inside the cut locus of and , then the energy density of is bounded by a constant depending only on , and . If , then is a constant map.
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Shiu
Yuen Cheng, Liouville theorem for harmonic maps, Geometry of
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Hawaii, 1979) Proc. Sympos. Pure Math., XXXVI, Amer. Math. Soc.,
Providence, R.I., 1980, pp. 147–151. MR 573431
(81i:58021)
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E. Greene and H.
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Notes in Mathematics, vol. 699, Springer, Berlin, 1979. MR 521983
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Stéfan
Hildebrandt, Helmut
Kaul, and KjellOve
Widman, An existence theorem for harmonic mappings of Riemannian
manifolds, Acta Math. 138 (1977), no. 12,
1–16. MR
0433502 (55 #6478)
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Shing
Tung Yau, Harmonic functions on complete Riemannian manifolds,
Comm. Pure Appl. Math. 28 (1975), 201–228. MR 0431040
(55 #4042)
 [1]
 S.Y. Cheng, Liouville theorem for harmonic maps, Proc. Sympos. Pure Math., vol. 36, Amer. Math. Soc., Providence, R. I., 1980, pp. 147151. MR 573431 (81i:58021)
 [2]
 R. Greene and H. Wu, Function theory of manifolds which possess a pole, Lecture Notes in Math., vol. 699, SpringerVerlag, Berlin and New York, 1979. MR 521983 (81a:53002)
 [3]
 S. Hildebrandt, H. Kaul and K.O. Widman, An existence theorem for harmonic mappings of Riemannian manifolds, Acta Math. 138 (1977), 116. MR 0433502 (55:6478)
 [4]
 S.T. Yau, Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math. 28 (1975), 201228. MR 0431040 (55:4042)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198206479053
PII:
S 00029939(1982)06479053
Article copyright:
© Copyright 1982
American Mathematical Society
