Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-30T20:05:35.070Z Has data issue: false hasContentIssue false
  • English
  • Français

On Eells-Sampson’s existence theorem for harmonic maps via exponentially harmonic maps

Published online by Cambridge University Press:  11 January 2016

Toshiaki Omori
Toshiaki Omori*
Affiliation:
Mathematical Institute Tohoku University, Sendai 980-8578, Japan, sa6m07@math.tohoku.ac.jp
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this note, we introduce an approximation of harmonic maps via a sequence of exponentially harmonic maps. We then reestablish the existence theorem of harmonic maps due to Eells and Sampson.

Keywords

53C4358J05
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 201 , March 2011 , pp. 133 - 146
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2011

References

[1] Duc, D. M., Variational problems of certain functionals, Internat. J. Math. 6 (1995), 503–535.Google Scholar
[2] Duc, D. M. and Eells, J., Regularity of exponentially harmonic functions, Internat. J. Math. 2 (1991), 395–408.Google Scholar
[3] Eells, J. and Lemaire, L., “Some properties of exponentially harmonic maps” in Partial Differential Equations, Part 1, 2 (Warsaw, 1990), Banach Center Publ. 27, Part 1, Vol. 2, Polish Acad. Sci., Warsaw, 1992, 129–136.Google Scholar
[4] Eells, J. and Sampson, J. H., Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1964), 109–160.Google Scholar
[5] Gilbarg, D. and Trudinger, N. S., Elliptic partial differential equations of second order, reprint of the 1998 original, Classics Math., Springer, Berlin, 2001.Google Scholar
[6] Hong, J. Q. and Yang, Y. H., Some results on exponentially harmonic maps(in Chinese), Chinese Ann. Math. Ser. A 14 (1993), 686–691.Google Scholar
[7] Lieberman, G. M., On the regularity of the minimizer of a functional with exponential growth, Comment. Math. Univ. Carolin. 33 (1992), 45–49.Google Scholar
[8] Naito, H., On a local Holder continuity for a minimizer of the exponential energy functional, Nagoya Math. J. 129 (1993), 97–113.Google Scholar