A finiteness theorem for Ricci curvature in dimension three

Zhu, Shun-Hui

doi:10.1090/S0273-0979-1990-15950-6

A finiteness theorem for Ricci curvature in dimension three

Author: Shun-Hui Zhu
Journal: Bull. Amer. Math. Soc. 23 (1990), 423-426
MSC (1985): Primary 53C20
DOI: https://doi.org/10.1090/S0273-0979-1990-15950-6
MathSciNet review: 1027905
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Uwe Abresch and Detlef Gromoll, On complete manifolds with nonnegative Ricci curvature, J. Amer. Math. Soc. 3 (1990), no. 2, 355–374. MR 1030656, https://doi.org/10.1090/S0894-0347-1990-1030656-6
Michael T. Anderson, Short geodesics and gravitational instantons, J. Differential Geom. 31 (1990), no. 1, 265–275. MR 1030673
Jeff Cheeger and Detlef Gromoll, The splitting theorem for manifolds of nonnegative Ricci curvature, J. Differential Geometry 6 (1971/72), 119–128. MR 0303460
Jeff Cheeger, Finiteness theorems for Riemannian manifolds, Amer. J. Math. 92 (1970), 61–74. MR 0263092, https://doi.org/10.2307/2373498
Karsten Grove and Peter Petersen V, Bounding homotopy types by geometry, Ann. of Math. (2) 128 (1988), no. 1, 195–206. MR 951512, https://doi.org/10.2307/1971439
K. Grove, P. Petersen V, and J. Y. Wu, Controlled topology in geometry, Bull. Amer. Math. Soc. (N.S.) 20 (1989), no. 2, 181–183. MR 974425, https://doi.org/10.1090/S0273-0979-1989-15755-8
John Hempel, 3-Manifolds, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1976. Ann. of Math. Studies, No. 86. MR 0415619
Stefan Peters, Cheeger’s finiteness theorem for diffeomorphism classes of Riemannian manifolds, J. Reine Angew. Math. 349 (1984), 77–82. MR 743966, https://doi.org/10.1515/crll.1984.349.77
Peter Petersen V, A finiteness theorem for metric spaces, J. Differential Geom. 31 (1990), no. 2, 387–395. MR 1037407
Richard Schoen and Shing Tung Yau, Complete three-dimensional manifolds with positive Ricci curvature and scalar curvature, Seminar on Differential Geometry, Ann. of Math. Stud., vol. 102, Princeton Univ. Press, Princeton, N.J., 1982, pp. 209–228. MR 645740
Zhong Min Shen, Finiteness and vanishing theorems for complete open Riemannian manifolds, Bull. Amer. Math. Soc. (N.S.) 21 (1989), no. 2, 241–244. MR 998628, https://doi.org/10.1090/S0273-0979-1989-15817-5
Ji-Ping Sha and DaGang Yang, Examples of manifolds of positive Ricci curvature, J. Differential Geom. 29 (1989), no. 1, 95–103. MR 978078
Alan Weinstein, On the homotopy type of positively-pinched manifolds, Arch. Math. (Basel) 18 (1967), 523–524. MR 0220311, https://doi.org/10.1007/BF01899493
Takao Yamaguchi, Homotopy type finiteness theorems for certain precompact families of Riemannian manifolds, Proc. Amer. Math. Soc. 102 (1988), no. 3, 660–666. MR 928999, https://doi.org/10.1090/S0002-9939-1988-0928999-X