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Equivariant minimax and minimal surfaces in geometric three-manifolds
Author(s):
Jon T.
Pitts;
J. H.
Rubinstein
Journal:
Bull. Amer. Math. Soc.
19
(1988),
303-309.
MSC (1985):
Primary 49F22, 53A10
MathSciNet review:
940493
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References:
- [HS] J. Hass and P. Scott, The existence of least area surfaces, preprint.
- [HL] W. Hsiang and H. B. Lawson, Minimal submanifolds of low cohomogeneity, J. Differential Geom. 5 (1971), 1-38. MR 298593
- [KPS] H. Karcher, U. Pinkall, and I. Sterling, New minimal surfaces in S3, preprint. MR 961512
- [LH] H. B. Lawson, Complete minimal surfaces in S3, Ann. of Math. (2) 90 (1970), 335-374.
- [MSY] W. Meeks, L. Simon, and S. T. Yau, Embedded minimal surfaces, exotic spheres, and manifolds with positive Ricci curvature, Ann. of Math. (2) 116 (1982), 621-659. MR 678484
- [OP] P. Orlik, Seifert fiber spaces, Lecture Notes in Math., vol. 291, Springer-Verlag, Berlin and New York, 1981.
- [PJ] J. Pitts, Existence and regularity of minimal surfaces on Riemannian manifolds, Math. Notes 27, Princeton Univ. Press, Princeton, N. J., 1981. MR 626027
- [PR1] J. Pitts and J. H. Rubinstein, Existence of minimal surfaces of bounded topological type in three-manifolds, Proceedings of the Centre for Mathematical Analysis 10 (1986), 163-176. MR 857665
- [PR2] J. Pitts and J. H. Rubinstein, Minimal surfaces of bounded topological type in three-manifolds, preprint.
- [PR3] J. Pitts and J. H. Rubinstein, Applications of minimax to minimal surfaces and the topology of 3-manifolds, Proc. Centre Math. Anal. 12 (1987), 137-170. MR 924434
- [SY] R. Schoen and S. T. Yau, Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with nonnegative scalar curvature, Ann. of Math. (2) 110 (1979), 127-145. MR 541332
- [SP1] P. Scott, The geometries of 3-manifolds, Bull. London Math. Soc. 15 (1983), 401-487. MR 705527
- [SP2] P. Scott, There are no false Seifert fibre spaces with infinite π1, Ann. of Math. (2) 117 (1983), 35-70.
- [SS] L. Simon and F. Smith, On the existence of embedded minimal 2-spheres in the 3-sphere, endowed with an arbitrary metric, preprint.
- [TW] W. Thurston, Geometry and topology of 3-manifolds, mimeographed lecture notes, Princeton Univ., 1978.
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Additional Information:
DOI:
10.1090/S0273-0979-1988-15652-2
PII:
S 0273-0979(1988)15652-2
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