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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Equivariant minimax and minimal surfaces in geometric three-manifolds
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by Jon T. Pitts and J. H. Rubinstein PDF
Bull. Amer. Math. Soc. 19 (1988), 303-309
References
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  • H. Karcher, U. Pinkall, and I. Sterling, New minimal surfaces in $S^3$, J. Differential Geom. 28 (1988), no. 2, 169–185. MR 961512, DOI 10.4310/jdg/1214442276
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  • 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, DOI 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.; University of Tokyo Press, Tokyo, 1981. MR 626027, DOI 10.1515/9781400856459
  • Jon T. Pitts and J. H. Rubinstein, Existence of minimal surfaces of bounded topological type in three-manifolds, Miniconference on geometry and partial differential equations (Canberra, 1985) Proc. Centre Math. Anal. Austral. Nat. Univ., vol. 10, Austral. Nat. Univ., Canberra, 1986, pp. 163–176. MR 857665
    • [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, Miniconference on geometry and partial differential equations, 2 (Canberra, 1986) Proc. Centre Math. Anal. Austral. Nat. Univ., vol. 12, Austral. Nat. Univ., Canberra, 1987, pp. 137–170. MR 924434
  • 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, DOI 10.2307/1971247
  • Peter Scott, The geometries of $3$-manifolds, Bull. London Math. Soc. 15 (1983), no. 5, 401–487. MR 705527, DOI 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.
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Additional Information
  • Journal: Bull. Amer. Math. Soc. 19 (1988), 303-309
  • MSC (1985): Primary 49F22, 53A10
  • DOI: https://doi.org/10.1090/S0273-0979-1988-15652-2
  • MathSciNet review: 940493