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Morse index of \(p\)-harmonic maps. (Indice de Morse des applications \(p\)-harmoniques.) (French) Zbl 0853.58037
Authors’ abstract: “We investigate estimates and calculation of the Morse index of \(p\)-harmonic maps, with \(p \in ]2,+\infty[\). More particularly, we deal with the identity map and maps from or to spheres. Our results extend those obtained for harmonic maps \((p = 2)\).
Full details are provided”.

MSC:
58E20 Harmonic maps, etc.
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References:
[1] J. Eells et L. Lemaire, Selected topics in harmonie maps, C.B.M.S. Regional Conf. Ser. 50, A.M.S., Providence, 1983. · Zbl 0515.58011
[2] El Soufi, A., Applications harmoniques, immersions minimales et transformations conformes de la sphère, Compositio Math., vol. 85, 281-298, (1993) · Zbl 0777.58010
[3] El Soufi, A., Indice de Morse des applications harmoniques de la sphère, Compositio Math., vol. 95, 343-362, (1995) · Zbl 0924.58012
[4] El Soufi, A.; Ilias, S., Immersions minimales, première valeur propre du laplacien et volume conforme, Math. Ann., vol. 275, 257-267, (1986) · Zbl 0675.53045
[5] El Soufi, A.; Ilias, S., Une inégalité du type « reilly » pour LES sous-variétés de l’espace hyperbolique, Comment. Math. Helv., vol. 67, 167-181, (1992) · Zbl 0758.53029
[6] El Soufi, A.; Jeune, A., Indice de Morse des applications p-harmoniques, C. R. Acad. Sci. Paris, t. 315, série I, 1189-1192, (1992) · Zbl 0769.58011
[7] A. Jeune, Thèse, Université de Tours, 1993.
[8] Leung, P. F., On the stability of harmonie maps, Lecture Notes in Math., n° 949, 122-129, (1982)
[9] Mazet, E., La formule de la variation seconde de l’énergie etc., J. Diff. Geom., vol. 8, 279-296, (1973) · Zbl 0301.53012
[10] Simons, J., Minimal varieties in Riemannian manifolds, Ann. of Math., vol. 88, 62-105, (1968) · Zbl 0181.49702
[11] Smith, R. T., The second variation formula for harmonic mappings, Proc. Amer. Math. Soc., vol. 47, 229-236, (1975) · Zbl 0303.58008
[12] Uhlenbeck, K., Minimal spheres and other conformai variationnal problems, Seminar on Minimal Submanifolds, 169-176, (1983), Princeton University press
[13] Xin, Y. L., Some results on stable harmonic maps, Duke Math. J., vol. 47, 609-613, (1980) · Zbl 0513.58019
[14] Yano, K.; Bochner, S., Curvature and Betti numbers, Ann. of Math. Studies, n° 32, (1953), Princeton Univ. press · Zbl 0051.39402
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