An energy estimate of an exterior problem and a Liouville theorem for harmonic maps
Zhang, Dong
Annales de l'I.H.P. Analyse non linéaire, Tome 11 (1994), p. 633-642 / Harvested from Numdam
Publié le : 1994-01-01
@article{AIHPC_1994__11_6_633_0,
     author = {Zhang, Dong},
     title = {An energy estimate of an exterior problem and a Liouville theorem for harmonic maps},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {11},
     year = {1994},
     pages = {633-642},
     mrnumber = {1310625},
     zbl = {0834.58017},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_1994__11_6_633_0}
}
Zhang, Dong. An energy estimate of an exterior problem and a Liouville theorem for harmonic maps. Annales de l'I.H.P. Analyse non linéaire, Tome 11 (1994) pp. 633-642. http://gdmltest.u-ga.fr/item/AIHPC_1994__11_6_633_0/

[An] M.T. Anderson, The Dirichlet Problem at Infinity for Manifolds of Negative Curvature, J. Diff. Geo., Vol. 18, 1983, pp. 701-721. | MR 730923 | Zbl 0541.53036

[Che] S.Y. Cheng, Liouville Theorem for Harmonic Maps, Proc. Sympos. Pure Math., Vol. 36, AMS, Providence, R.I., 1980, pp. 147-151. | MR 573431 | Zbl 0455.58009

[Cho] H.I. Choi, On the Liouville Theorem for Harmonic Maps, Proc. of AMS, Vol. 85, No. 1, 1980, pp. 91-94. | MR 647905 | Zbl 0485.53038

[E-L] J. Eells Jr and L. Lemaire, Another Report on Harmonic Maps, Bull. London Math. Soc., Vol. 20, 1988, pp. 385-524. | MR 956352 | Zbl 0669.58009

[E-S] J. Eells Jr. and J.H. Sampson, Harmonic Mappings of Riemannian Manifolds, Amer. J. Math., Vol. 86, 1964, pp. 109-160. | MR 164306 | Zbl 0122.40102

[GH] M. Giaquinta and S. Hildebrandt, A priori Estimates for Harmonic Mappings. J. Reine Angew. Math., Vol. 336, 1982, pp. 124-164. | MR 671325 | Zbl 0508.58015

[Hi] S. Hildebrandt, Liouville Theorems for Harmonic Maps and an Approach to Beinstein Theorems, Ann. of Math. Studies, Vol. 102, 1982, S. T. Yau ed., pp. 107-131. | MR 645732 | Zbl 0505.58014

[H-J-W] S. Hildebrandt, J. Jost and K.O. Widman, Harmonic Mappings and Minimal Submanifolds. Inventiones Math., Vol. 62, 1980, pp. 269-298. | MR 595589 | Zbl 0446.58006

[H-K-W] S. Hildebrandt, H. Kaul and K.O. Widman, An Existence Theory for Harmonic Mappings of Riemannian Manifolds. Acta Math., Vol. 138, 1977, pp. 1-16. | MR 433502 | Zbl 0356.53015

[Ji] Z. Jin, Liouville Theorems for Harmonic Maps, Inventiones Math., to appear. | MR 1156381 | Zbl 0768.53016

[Sc] R. Schoen, Analytic Aspects of the Harmonic Map Problem, Seminar on Non-linear PDE, S. S. Cherned. ed, pp. 321-358. | MR 765241 | Zbl 0551.58011

[Se] H.C.J. Sealey, Some Conditions Ensuring the Vanishing of Harmonic Differential Forms with Applications to Harmonic Maps and Yang-Mills Theory, Math. Proc. Camb. Phil. Soc. Vol. 91, 1982, pp. 441-452. | MR 654088 | Zbl 0494.58002

[S-U] R. Schoen and K. Uhlenbeck, A Regularity Theory for Harmonic Maps, J. Diff. Geom., Vol. 60, 1984, pp. 307-335. | MR 664498 | Zbl 0521.58021

[Su] D. Sullivan, The Dirichlet Problem at Infinity for a Negatively Curved Manifold, J. Diff. Geo., Vol. 18, 1983, pp. 723-732. | MR 730924 | Zbl 0541.53037

[S-Y] R. Schoen and S.T. Yau, Harmonic Maps and the Topology of Stable Hypersurfaces and Manifolds with non-negative Ricci Curvature, Comm. Math. Helv., Vol. 51, 1976, pp. 333-341. | MR 438388 | Zbl 0361.53040

[Ya] S.T. Yau, Harmonic Functions on Complete Riemannian Manifolds, Comm. Pure Appl. Math., Vol. 28, 1975, pp. 201-228. | MR 431040 | Zbl 0291.31002