An energy estimate of an exterior problem and a Liouville theorem for harmonic maps

Dong Zhang

Annales de l'I.H.P. Analyse non linéaire (1994)

  • Volume: 11, Issue: 6, page 633-642
  • ISSN: 0294-1449

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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 11.6 (1994): 633-642. <http://eudml.org/doc/78346>.

@article{Zhang1994,
author = {Zhang, Dong},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {energy estimate; Liouville theorem; harmonic maps; Euclidean space; Riemannian manifolds},
language = {eng},
number = {6},
pages = {633-642},
publisher = {Gauthier-Villars},
title = {An energy estimate of an exterior problem and a Liouville theorem for harmonic maps},
url = {http://eudml.org/doc/78346},
volume = {11},
year = {1994},
}

TY - JOUR
AU - Zhang, Dong
TI - An energy estimate of an exterior problem and a Liouville theorem for harmonic maps
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1994
PB - Gauthier-Villars
VL - 11
IS - 6
SP - 633
EP - 642
LA - eng
KW - energy estimate; Liouville theorem; harmonic maps; Euclidean space; Riemannian manifolds
UR - http://eudml.org/doc/78346
ER -

References

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  2. [Che] S.Y. Cheng, Liouville Theorem for Harmonic Maps, Proc. Sympos. Pure Math., Vol. 36, AMS, Providence, R.I., 1980, pp. 147-151. Zbl0455.58009MR573431
  3. [Cho] H.I. Choi, On the Liouville Theorem for Harmonic Maps, Proc. of AMS, Vol. 85, No. 1, 1980, pp. 91-94. Zbl0485.53038MR647905
  4. [E-L] J. Eells Jr and L. Lemaire, Another Report on Harmonic Maps, Bull. London Math. Soc., Vol. 20, 1988, pp. 385-524. Zbl0669.58009MR956352
  5. [E-S] J. Eells Jr. and J.H. Sampson, Harmonic Mappings of Riemannian Manifolds, Amer. J. Math., Vol. 86, 1964, pp. 109-160. Zbl0122.40102MR164306
  6. [GH] M. Giaquinta and S. Hildebrandt, A priori Estimates for Harmonic Mappings. J. Reine Angew. Math., Vol. 336, 1982, pp. 124-164. Zbl0508.58015MR671325
  7. [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. Zbl0505.58014MR645732
  8. [H-J-W] S. Hildebrandt, J. Jost and K.O. Widman, Harmonic Mappings and Minimal Submanifolds. Inventiones Math., Vol. 62, 1980, pp. 269-298. Zbl0446.58006MR595589
  9. [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. Zbl0356.53015MR433502
  10. [Ji] Z. Jin, Liouville Theorems for Harmonic Maps, Inventiones Math., to appear. Zbl0768.53016MR1156381
  11. [Sc] R. Schoen, Analytic Aspects of the Harmonic Map Problem, Seminar on Non-linear PDE, S. S. Cherned. ed, pp. 321-358. Zbl0551.58011MR765241
  12. [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. Zbl0494.58002MR654088
  13. [S-U] R. Schoen and K. Uhlenbeck, A Regularity Theory for Harmonic Maps, J. Diff. Geom., Vol. 60, 1984, pp. 307-335. Zbl0521.58021MR664498
  14. [Su] D. Sullivan, The Dirichlet Problem at Infinity for a Negatively Curved Manifold, J. Diff. Geo., Vol. 18, 1983, pp. 723-732. Zbl0541.53037MR730924
  15. [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. Zbl0361.53040MR438388
  16. [Ya] S.T. Yau, Harmonic Functions on Complete Riemannian Manifolds, Comm. Pure Appl. Math., Vol. 28, 1975, pp. 201-228. Zbl0291.31002MR431040

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