Liouville type theorems and regularity of harmonic maps

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.
Chapter Google Scholar
J.Eells and L.Lemaire, "Selected topics in harmonic maps", CBMS 50. Published by the American Mathemalical Society, 1983.
Google Scholar
J. Eells and J.H. Sampson, "Harmonic mappings of Riemannian manifolds", Amer. J.Math. 86 (1964), 109–160.
Article MathSciNet MATH Google Scholar
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.
Book Google Scholar
J.H.Sampson, "On harmonic mappings", lstituto Nazionale di Alta Math., Sympo. Math., Vol. XXVI, Monograf Bologna, 1982.
Google Scholar
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.
Article MathSciNet MATH Google Scholar
H.C.J.Sealey, "The stress-energy tensor and vanishing of L² harmonic forms", Preprint.
Google Scholar
J. Simons, "Minimal varietes in Riemannian manifolds", Ann. of Math. 88(1968), 62–105.
Article MathSciNet MATH Google Scholar
R. Schoen and K. Uhlenbeck, "A regularity theorem for harmonic maps", J.Diff. Geom. 17(1982), 307–335.
MathSciNet MATH Google Scholar
R. Schoen and K. Uhlenbeck, "Regularity of minimizing harmonic maps into the sphere", Invent. Math. 78(1984), 89–100.
Article MathSciNet MATH Google Scholar
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
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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Institute of Mathematics, Fudan University, China
Y. L. Xin

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Y. L. Xin
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Chaohao Gu Marcel Berger Robert L. Bryant

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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
Published: 19 September 2006
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-17849-1
Online ISBN: 978-3-540-47883-6
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