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Every three-sphere of positive Ricci curvature contains a minimal embedded torus
Author(s):
Brian
White
Journal:
Bull. Amer. Math. Soc.
21
(1989),
71-75.
MSC (1980):
Primary 58E12, 53A10, 49F10
MathSciNet review:
994891
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References:
- [CS] H. I. Choi and R. Schoen, The space of minimal embeddings of a surface into a three dimensional manifold of positive ricci curvature, Invent. Math. 81 (1985), 387-394. MR 807063
- [H] R. Hamilton, Three-manifolds with positive ricci curvature, J. Differential Geom. 17 (1982), 255-306. MR 664497
- [J] J. Jost, Embedded minimal surfaces in manifolds diffeomorphic to the three dimensional ball or sphere, preprint. MR 1010172
- [L] H. B. Lawson, Complete minimal surfaces in S, Ann. of Math. (2) 92 (1970), 335-374. MR 270280
- [P] J. Pitts, Existence and regularity of minimal surfaces on riemannian manifolds, Princeton Univ. Press, Princeton, N.J., 1981. MR 626027
- [PR] J. Pitts and H. Rubinstein, Equivariant minimax and minimal surfaces in geometric 3-manifolds, Bull. Amer. Math. Soc. (N.S.) 19 (1988), 303-309. MR 940493
- [SS2] L. Simon and F. Smith, On the existence of embedded minimal two-spheres in the three-sphere, endowed with an arbitrary riemannian metric, preprint.
- [TT] F. Tomi and A. J. Tromba, Extreme curves bound embedded minimal surfaces of the type of the disk, Math. Z. 158 (1978), 137-145. MR 486522
- [Wl] B. White, New applications of mapping degrees to minimal surface theory, J. Differential Geom. 29 (1989), 143-152. MR 978083
- [W2] B. White, The space of minimal submanifolds for varying riemannian metrics, preprint. MR 1101226
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Additional Information:
DOI:
10.1090/S0273-0979-1989-15765-0
PII:
S 0273-0979(1989)15765-0
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