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Liouville type theorems and regularity of harmonic maps

Part of the Lecture Notes in Mathematics book series (LNM,volume 1255)

Keywords

  • Riemannian Manifold
  • Sectional Curvature
  • Compact Riemannian Manifold
  • Regularity Theorem
  • Local Orthonormal Frame

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References

  1. P. Baird and J. Eells, "A conservation law for harmonic maps", Geom. Sympos. (Utrecht, 1980), Lecture Notes in Math. Vol. 894, Springer-Verlag, Berlin and New York, 1980, 1–15.

    CrossRef  Google Scholar 

  2. J.Eells and L.Lemaire, "Selected topics in harmonic maps", CBMS 50. Published by the American Mathemalical Society, 1983.

    Google Scholar 

  3. J. Eells and J.H. Sampson, "Harmonic mappings of Riemannian manifolds", Amer. J.Math. 86 (1964), 109–160.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. R.E. Green and H. Wu, "Function theory on manifolds which possess a pole" Lecture Notes in Math. Vol. 699, Springer-Verlag, Berlin and New York, 1979.

    CrossRef  Google Scholar 

  5. J.H.Sampson, "On harmonic mappings", lstituto Nazionale di Alta Math., Sympo. Math., Vol. XXVI, Monograf Bologna, 1982.

    Google Scholar 

  6. H.C. Sealey, "Some condition ensuring the vanishing of harmonic differential forms with applications to harmonic maps and Yang-Mills theory" Math. Proc. Camb. Phil. Soc. 91(1982), 441–452.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. H.C.J.Sealey, "The stress-energy tensor and vanishing of L2 harmonic forms", Preprint.

    Google Scholar 

  8. J. Simons, "Minimal varietes in Riemannian manifolds", Ann. of Math. 88(1968), 62–105.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. R. Schoen and K. Uhlenbeck, "A regularity theorem for harmonic maps", J.Diff. Geom. 17(1982), 307–335.

    MathSciNet  MATH  Google Scholar 

  10. R. Schoen and K. Uhlenbeck, "Regularity of minimizing harmonic maps into the sphere", Invent. Math. 78(1984), 89–100.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Y.L.Xin, "Nonexistence and existence for harmonic maps in Riemannian manifolds", Proc. 1981 Shanghai-Hefei Symposium on Differential Geometry and Differential Equations, Science Press, 1984.

    Google Scholar 

  12. Y.L. Xin, "Differential forms, conservation law and monotonicity formula", Scientia Sinica (Ser A) V. XXIX (1) (1986), 40–50.

    MathSciNet  MATH  Google Scholar 

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© 1987 Springer-Verlag

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Xin, Y.L. (1987). Liouville type theorems and regularity of harmonic maps. In: Gu, C., Berger, M., Bryant, R.L. (eds) Differential Geometry and Differential Equations. Lecture Notes in Mathematics, vol 1255. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0077691

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  • DOI: https://doi.org/10.1007/BFb0077691

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17849-1

  • Online ISBN: 978-3-540-47883-6

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