References
Bérard, P.H.: Remarques sur l'equation de J. Simons. In: Lawson, B., Tenenblat, K. (eds.) Differential geometry. Harlow: Longman 1991
do Carmo, M., Peng, C.K.: Stable complete minimal hypersurfaces. In: Chern, S.S., Tsun, W.W. (eds.) Proceedings of the 1980 Beijing Symposium on Differential Geometry and Differential Equations. Beijing: Science Press 1982
Eells, J., Lemaire, L.: A report on harmonic maps. Bull. Lond. Math. Soc.10, 1–68 (1978)
Grove, K., Karcher, H., Ruh, E.A.: Jacobi fields and Finsler metrics on compact Lie groups with an application to differential pinching problems. Math. Ann.211, 7–21 (1974)
Helgason, S.: Differential geometry, Lie groups and symmetric spaces. New York San Francisco London: Academic Press 1978
Howard, R., Wei, S.W.: Nonexistence of stable harmonic maps to and from certain homogeneous spaces and submanifolds of Euclidean space. Trans. Am. Math. Soc.294, 319–331 (1986)
Nakajima, H.: Regularity of minimizing harmonic maps into certain Riemannian manifolds. Preprint
Nakajima, H.: Yau's trick. Sugaku.41, 253–258 (1989) (in Japanese)
Ohnita, Y.: Stability of harmonic maps and standard minimal immersions. Tôhoku Math. J.38, 259–267 (1986)
Ohnita, Y.: On stability of minimal submanifolds in compact symmetric spaces. Compos. Math.64, 157–189 (1987)
Okayasu, T.: Pinching and nonexistence of stable harmonic maps. Tôhoku Math. J.40, 213–220 (1988)
Okayasu, T.: Generalized Kato's inequality for minimal submanifolds and its application. (in preparation)
Schoen, R., Simon, L., Yau, S.T.: Curvature estimates for minimal hypersurfaces. Acta Math.134, 275–288 (1975)
Schoen, R., Uhlenbeck, K.: A regularity theory for harmonic maps. J. Differ. Geom.17, 307–335 (1982)
Schoen, R., Uhlenbeck, K.: Regularity of minimizing harmonic maps into the sphere. Invent. Math.78, 89–100 (1984)
Simons, J.: Minimal varieties in Riemannian manifolds. Ann. Math.88, 62–105 (1968)
Urakawa, H.: The first eigenvalue of the Laplacian for a positively curved homogeneous Riemannian manifold. Compos. Math.59, 57–71 (1986)
Xin, Y.L.: Regularity of harmonic maps into certain homogeneous spaces. (Lect. Notes Math. vol. 1369, pp. 295–305). Berlin Heidelberg New York: Springer 1989
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Okayasu, T. Regularity of minimizing harmonic maps intoS 4,S 5 and symmetric spaces. Math. Ann. 298, 193–205 (1994). https://doi.org/10.1007/BF01459734
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DOI: https://doi.org/10.1007/BF01459734