Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

Equivariant minimax and minimal surfaces in geometric three-manifolds


Authors: Jon T. Pitts and J. H. Rubinstein
Journal: Bull. Amer. Math. Soc. 19 (1988), 303-309
MSC (1985): Primary 49F22, 53A10
MathSciNet review: 940493
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [HS] J. Hass and P. Scott, The existence of least area surfaces, preprint.
  • Wu-yi Hsiang and H. Blaine Lawson Jr., Minimal submanifolds of low cohomogeneity, J. Differential Geometry 5 (1971), 1–38. MR 0298593 (45 #7645)
  • H. Karcher, U. Pinkall, and I. Sterling, New minimal surfaces in 𝑆³, J. Differential Geom. 28 (1988), no. 2, 169–185. MR 961512 (89j:53050)
  • [LH] H. B. Lawson, Complete minimal surfaces in S3, Ann. of Math. (2) 90 (1970), 335-374.
  • William Meeks III, Leon Simon, and Shing Tung Yau, Embedded minimal surfaces, exotic spheres, and manifolds with positive Ricci curvature, Ann. of Math. (2) 116 (1982), no. 3, 621–659. MR 678484 (84f:53053), http://dx.doi.org/10.2307/2007026
  • [OP] P. Orlik, Seifert fiber spaces, Lecture Notes in Math., vol. 291, Springer-Verlag, Berlin and New York, 1981.
  • Jon T. Pitts, Existence and regularity of minimal surfaces on Riemannian manifolds, Mathematical Notes, vol. 27, Princeton University Press, Princeton, N.J., 1981. MR 626027 (83e:49079)
  • Jon T. Pitts and J. H. Rubinstein, Existence of minimal surfaces of bounded topological type in three-manifolds, (Canberra, 1985) Proc. Centre Math. Anal. Austral. Nat. Univ., vol. 10, Austral. Nat. Univ., Canberra, 1986, pp. 163–176. MR 857665 (87j:49074)
  • [PR2] J. Pitts and J. H. Rubinstein, Minimal surfaces of bounded topological type in three-manifolds, preprint.
  • Jon T. Pitts and J. H. Rubinstein, Applications of minimax to minimal surfaces and the topology of 3-manifolds, (Canberra, 1986) Proc. Centre Math. Anal. Austral. Nat. Univ., vol. 12, Austral. Nat. Univ., Canberra, 1987, pp. 137–170. MR 924434 (89a:57001)
  • R. Schoen and Shing Tung Yau, Existence of incompressible minimal surfaces and the topology of three-dimensional manifolds with nonnegative scalar curvature, Ann. of Math. (2) 110 (1979), no. 1, 127–142. MR 541332 (81k:58029), http://dx.doi.org/10.2307/1971247
  • Peter Scott, The geometries of 3-manifolds, Bull. London Math. Soc. 15 (1983), no. 5, 401–487. MR 705527 (84m:57009), http://dx.doi.org/10.1112/blms/15.5.401
  • [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.

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1985): 49F22, 53A10

Retrieve articles in all journals with MSC (1985): 49F22, 53A10


Additional Information

DOI: http://dx.doi.org/10.1090/S0273-0979-1988-15652-2
PII: S 0273-0979(1988)15652-2