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Minimal surfaces with low index in the three-dimensional sphere

Author: Francisco Urbano
Journal: Proc. Amer. Math. Soc. 108 (1990), 989-992
MSC: Primary 53C40
MathSciNet review: 1007516
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Abstract: In the present paper, the author gives a characterization of the Clifford torus among the minimal surfaces of the three-dimensional sphere in terms of its index.

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  • [A] F. J. Almgren, Jr., Some interior regularity theorems for minimal surfaces and an extension of Berstein's theorem, Ann. of Math. 84 (1966), 277-292. MR 0200816 (34:702)
  • [Ch-DoC-K] S. S. Chern, M. DoCarmo, and S. Kobayashi, Minimal submanifolds of a sphere with second fundamental form of constant length, Functional Analysis and Related Fields, Proc. Conf. M. Stone, Springer, 1970, pp. 59-75. MR 0273546 (42:8424)
  • [FC] D. Fischer-Colbrie, On complete minimal surfaces with finite Morse index in three manifolds, Invent. Math. 82 (1985), 121-132. MR 808112 (87b:53090)
  • [L-Y] P. Li and S. T. Yau, A new conformal invariant and its applications to the Willmore conjecture and first eigenvalue of compact surfaces, Invent. Math. 69 (1982), 269-291. MR 674407 (84f:53049)
  • [L-R] F. J. Lopez and A. Ros, Complete minimal surfaces with index one and stable constant mean curvature surfaces, Comment. Math. Helvetici 64 (1989), 34-43. MR 982560 (90b:53006)
  • [M-R] S. Montiel and A. Ros, Minimal immersions of surfaces by the first eigenfunctions and conformal area, Invent. Math. 83 (1986), 153-166. MR 813585 (87d:53109)
  • [O] M. Obata, Certain conditions for a Riemannian manifold to be isometric with a sphere, J. Math. Soc. Japan 14 (1962), 333-340. MR 0142086 (25:5479)
  • [S] J. Simons, Minimal varieties in Riemannian manifolds, Ann. of Math. 88 (1968), 62-105. MR 0233295 (38:1617)

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Keywords: Minimal surface, index, Jacobi operator
Article copyright: © Copyright 1990 American Mathematical Society

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