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Regularity of harmonic maps into certain homogeneous spaces

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Differential Geometry and Topology

Part of the book series: Lecture Notes in Mathematics ((2803,volume 1369))

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References

  1. J. Eells and L. Lemaire: "Selected topics in harmonic maps" CBMS n.50, 1983.

    Google Scholar 

  2. D. Fischer-Colbrie and R. Schoen: "The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature" Comm. Pure Appl. Math. 33(1980), 199–211.

    Article  MathSciNet  MATH  Google Scholar 

  3. R. Howard and S.W. Wei: "Nonexistence of stable harmonic maps to and from certain homogeneous spaces and submanifolds of Euclidean space" Trans. A.M.S. 294(1) (1986), 319–331.

    Article  MathSciNet  MATH  Google Scholar 

  4. L. Karp: "Subharmonic function, harmonic mappings and isometric immersions" Seminar on differential geometry, Ann. Math. Studies 102, Princeton Univ. Press.

    Google Scholar 

  5. T. Nagano: "Stability of harmonic maps between symmetric spaces" Lecture Notes Math. 949,Springer-Verlag. (1982), 130–137.

    Google Scholar 

  6. Y. Ohnita: "Stability of harmonic maps and standard minimal immersions" Tôhoku Math. J. 38(1986), 259–267.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  8. R. Schoen, L. Simon and S.T. Yau: "Curvature estimates for minimal hypersurfaces" Acta Math. 134(1975),275–288.

    Article  MathSciNet  MATH  Google Scholar 

  9. R. Schoen and K. Uhlenbeck: "A regularity theory 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.

    Article  MathSciNet  MATH  Google Scholar 

  11. Y.L. Xin: "Liouville type theorems and regularity of harmonic maps" Proc. DD6 Symp. Lecture Notes Math. 1255. Springer-Verlag (1987).

    Google Scholar 

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Boju Jiang Chia-Kuei Peng Zixin Hou

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© 1989 Springer-Verlag

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Xin, YL. (1989). Regularity of harmonic maps into certain homogeneous spaces. In: Jiang, B., Peng, CK., Hou, Z. (eds) Differential Geometry and Topology. Lecture Notes in Mathematics, vol 1369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087543

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  • DOI: https://doi.org/10.1007/BFb0087543

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51037-6

  • Online ISBN: 978-3-540-46137-1

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