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On the existence of global solutions of the nonlinear parabolic equation of Eells-Sampson over product manifolds


Author: Seiki Nishikawa
Journal: Proc. Amer. Math. Soc. 82 (1981), 369-373
MSC: Primary 58E20; Secondary 35K55
DOI: https://doi.org/10.1090/S0002-9939-1981-0612721-4
MathSciNet review: 612721
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Abstract: We extend results of Lemaire and Hamilton on the existence of global solutions of the equation in the title to warped product manifolds with boundaries.


References [Enhancements On Off] (What's this?)

  • [1] R. L. Bishop and B. O'Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc. 145 (1969), 1-49. MR 0251664 (40:4891)
  • [2] J. Eells and J. H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1964), 109-160. MR 0164306 (29:1603)
  • [3] R. S. Hamilton, Harmonic maps of manifolds with boundary, Lecture Notes in Math., vol. 471, Springer-Verlag, Berlin and New York, 1975. MR 0482822 (58:2872)
  • [4] L. Lemaire, Applications harmonique de variétés produits, Comment. Math. Helv. 52 (1977), 11-24. MR 0448411 (56:6718)
  • [5] S. Nishikawa, On the Neumann problem for the nonlinear parabolic equation of Eells-Sampson and harmonic mappings, Math. Ann. 249 (1980), 177-190. MR 578724 (81k:58031)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0612721-4
Keywords: Nonlinear parabolic equation of Eells-Sampson, harmonic map, warped product
Article copyright: © Copyright 1981 American Mathematical Society

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