Estimates on the stability of minimal surfaces and harmonic maps

Makoto SAKAKI

doi:10.2969/jmsj/04140641

Makoto SAKAKI

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JOURNAL FREE ACCESS

1989 Volume 41 Issue 4 Pages 641-650

DOI https://doi.org/10.2969/jmsj/04140641

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Published: 1989 Received: April 22, 1988 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) J. L. Barbosa and M. do Carmo, Stability of minimal surfaces and eigenvalues of the Laplacian, Math. Z., 173 (1980), 13-28.
2) J. L. Barbosa and M. do Carmo, Stability of minimal surfaces in spaces of constant curvature, Bol. Soc. Brasil. Math., 11 (1980), 1-10.
3) M. Berger, Sur quelques varietes Riemanniennes suffisamment pincees, Bull. Soc. Math. France, 88 (1960), 57-71.
4) J. Eells and L. Lemaire, Selected Topics in Harmonic Maps, CBMC Regional Conf.Ser., 50, Amer. Math. Soc., 1983.
5) D. Hoffman, Lower bounds on the first eigenvalue of the Laplacian of Riemannian submanifolds, Minimal submanifolds and geodesics, Kaigai Publ., Tokyo, 1978, pp. 61-73.
6) D. Hoffman and R. Osserman, The area of the generalized Gaussian image and the stability of minimal surfaces in Sⁿ and Rⁿ, Math. Ann., 260 (1982), 437-452.
7) G. R. Jensen and M. Rigoli, Harmonic Gauss maps, Pacific J. Math., 136 (1989), 261-282.
8) K. Ogiue, Differential geometry of Kaehler submanifolds, Adv. in Math., 13 (1974), 73-114.
9) M. Sakaki, Remarks on the rigidity and stability of minimal submanifolds, to appear in Proc. Amer. Math. Soc.
10) J. Simons, Minimal varietes in riemannian manifolds, Ann. of Math., 88 (1968), 62-105.
11) J. Spruck, Remarks on the stability of minimal submanifolds of Rⁿ, Math. Z., 144 (1975), 169-174.
12) S. Tanno, Remarks on Sobolev inequalities and stability of minimal submanifolds, J. Math. Soc. Japan, 35 (1983), 323-329.
13) J. A. Wolf, Spaces of constant curvature, McGraw-Hill, New-York, 1967.

Right : [1] J. L. Barbosa and M. do Carmo, Stability of minimal surfaces and eigenvalues of the Laplacian, Math. Z., 173 (1980), 13-28.
[2] J. L. Barbosa and M. do Carmo, Stability of minimal surfaces in spaces of constant curvature, Bol. Soc. Brasil. Math., 11 (1980), 1-10.
[3] M. Berger, Sur quelques varietes Riemanniennes suffisamment pincees, Bull. Soc. Math. France, 88 (1960), 57-71.
[4] J. Eells and L. Lemaire, Selected Topics in Harmonic Maps, CBMC Regional Conf. Ser., 50, Amer. Math. Soc., 1983.
[5] D. Hoffman, Lower bounds on the first eigenvalue of the Laplacian of Riemannian submanifolds, Minimal submanifolds and geodesics, Kaigai Publ., Tokyo, 1978, pp. 61-73.
[6] D. Hoffman and R. Osserman, The area of the generalized Gaussian image and the stability of minimal surfaces in Sⁿ and Rⁿ, Math. Ann., 260 (1982), 437-452.
[7] G. R. Jensen and M. Rigoli, Harmonic Gauss maps, Pacific J. Math., 136 (1989), 261-282.
[8] K. Ogiue, Differential geometry of Kaehler submanifolds, Adv. in Math., 13 (1974), 73-114.
[9] M. Sakaki, Remarks on the rigidity and stability of minimal submanifolds, to appear in Proc. Amer. Math. Soc.
[10] J. Simons, Minimal varietes in riemannian manifolds, Ann. of Math., 88 (1968), 62-105.
[11] J. Spruck, Remarks on the stability of minimal submanifolds of Rⁿ, Math. Z., 144 (1975), 169-174.
[12] S. Tanno, Remarks on Sobolev inequalities and stability of minimal submanifolds, J. Math. Soc. Japan, 35 (1983), 323-329.
[13] J. A. Wolf, Spaces of constant curvature, McGraw-Hill, New-York, 1967.

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