A Bochner theorem and applications
Xiaochun Rong
Source: Duke Math. J. Volume 91, Number 2
(1998), 381-392.
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References
[Ab] U. Abrech, Uber das glatten Riemannn'scher metriken, Habilitationesschrift, Reinischen Friedrisch-Wilhelms-Universitat, Bonn, 1988.
[An] M. Anderson, private communication, n.d.
[AC] M. Anderson and J. Cheeger, $C\sp \alpha$-compactness for manifolds with Ricci curvature and injectivity radius bounded below, J. Differential Geom. 35 (1992), no. 2, 265–281.
Mathematical Reviews (MathSciNet): MR93c:53028
Zentralblatt MATH: 0774.53021
Project Euclid: euclid.jdg/1214448075
[Ba] S. Bando, Real analyticity of solutions of Hamilton's equation, Math. Z. 195 (1987), no. 1, 93–97.
Mathematical Reviews (MathSciNet): MR88i:53073
Zentralblatt MATH: 0606.58051
Digital Object Identifier: doi:10.1007/BF01161602
[BMR] J. Bemelmans, [M.] Min-Oo, and E. Ruh, Smoothing Riemannian metrics, Math. Z. 188 (1984), no. 1, 69–74.
Mathematical Reviews (MathSciNet): MR85m:58184
Zentralblatt MATH: 0536.53044
Digital Object Identifier: doi:10.1007/BF01163873
[Br] G. Bredon, Introduction to compact transformation groups, Pure and Applied Mathematics, vol. 46, Academic Press, New York, 1972.
Mathematical Reviews (MathSciNet): MR54:1265
Zentralblatt MATH: 0246.57017
[Ch] J. Cheeger, Finiteness Theorems for Riemannian Manifolds, Amer. J. Math. 92 (1970), 61–74.
Mathematical Reviews (MathSciNet): MR41:7697
Zentralblatt MATH: 0194.52902
Digital Object Identifier: doi:10.2307/2373498
JSTOR: links.jstor.org
[CE] J. Cheeger and D. Ebin, Comparison theorems in Riemannian geometry, North-Holland Mathematical Library, vol. 9, North-Holland Publishing Co., Amsterdam, 1975.
Mathematical Reviews (MathSciNet): MR56:16538
Zentralblatt MATH: 0309.53035
[CFG] J. Cheeger, K. Fukaya, and M. Gromov, Nilpotent structures and invariant metrics on collapsed manifolds, J. Amer. Math. Soc. 5 (1992), no. 2, 327–372.
Mathematical Reviews (MathSciNet): MR93a:53036
Zentralblatt MATH: 0758.53022
Digital Object Identifier: doi:10.2307/2152771
JSTOR: links.jstor.org
[CG1] J. Cheeger and M. Gromov, Collapsing Riemannian manifolds while keeping their curvature bounded. I, J. Differential Geom. 23 (1986), no. 3, 309–346.
Mathematical Reviews (MathSciNet): MR87k:53087
Zentralblatt MATH: 0606.53028
Project Euclid: euclid.jdg/1214440117
[CG2] J. Cheeger and M. Gromov, Collapsing Riemannian manifolds while keeping their curvature bounded. II, J. Differential Geom. 32 (1990), no. 1, 269–298.
Mathematical Reviews (MathSciNet): MR92a:53066
Zentralblatt MATH: 0727.53043
Project Euclid: euclid.jdg/1214445047
[CG3] J. Cheeger and M. Gromov, On the characteristic numbers of complete manifolds of bounded curvature and finite volume, Differential geometry and complex analysis, Springer, Berlin, 1985, pp. 115–154.
Mathematical Reviews (MathSciNet): MR86h:58131
Zentralblatt MATH: 0592.53036
[CR1] J. Cheeger and X. Rong, Collapsed Riemannian manifolds with bounded diameter and bounded covering geometry, Geom. Funct. Anal. 5 (1995), no. 2, 141–163.
Mathematical Reviews (MathSciNet): MR96h:53053
Zentralblatt MATH: 0843.53039
Digital Object Identifier: doi:10.1007/BF01895665
[CR2] J. Cheeger and X. Rong, Existence of polarized $F$-structures on collapsed manifolds with bounded curvature and diameter, Geom. Funct. Anal. 6 (1996), no. 3, 411–429.
Mathematical Reviews (MathSciNet): MR97f:53074
Zentralblatt MATH: 0863.53026
Digital Object Identifier: doi:10.1007/BF02249258
[DSW] X. Dai, Z. Shen, and G. Wei, Negative Ricci curvature and isometry group, Duke Math. J. 76 (1994), no. 1, 59–73.
Mathematical Reviews (MathSciNet): MR96e:53051
Zentralblatt MATH: 0820.53045
Digital Object Identifier: doi:10.1215/S0012-7094-94-07603-5
Project Euclid: euclid.dmj/1077286739
[DWY] X. Dai, G. Wei, and R. Ye, Smoothing Riemannian metrics with Ricci curvature bounds, Manuscripta Math. 90 (1996), no. 1, 49–61.
Mathematical Reviews (MathSciNet): MR97b:53039
Zentralblatt MATH: 0880.53034
Digital Object Identifier: doi:10.1007/BF02568293
[Fu1] K. Fukaya, Collapsing Riemannian manifolds to ones of lower dimensions, J. Differential Geom. 25 (1987), no. 1, 139–156.
Mathematical Reviews (MathSciNet): MR88b:53050
Zentralblatt MATH: 0606.53027
Project Euclid: euclid.jdg/1214440728
[Fu2] K. Fukaya, A boundary of the set of the Riemannian manifolds with bounded curvatures and diameters, J. Differential Geom. 28 (1988), no. 1, 1–21.
Mathematical Reviews (MathSciNet): MR89h:53090
Zentralblatt MATH: 0652.53031
Project Euclid: euclid.jdg/1214442157
[Fu3] K. Fukaya, Collapsing Riemannian manifolds to ones with lower dimension. II, J. Math. Soc. Japan 41 (1989), no. 2, 333–356.
Mathematical Reviews (MathSciNet): MR90c:53103
Zentralblatt MATH: 0703.53042
Digital Object Identifier: doi:10.2969/jmsj/04120333
Project Euclid: euclid.jmsj/1230128772
[Fu4] K. Fukaya, Hausdorff convergence of Riemannian manifolds and its applications, Recent topics in differential and analytic geometry, Adv. Stud. Pure Math., vol. 18, Academic Press, Boston, MA, 1990, pp. 143–238.
Mathematical Reviews (MathSciNet): MR92k:53076
Zentralblatt MATH: 0754.53004
[GY] L. Z. Gao and S.-T. Yau, The existence of negatively Ricci curved metrics on three-manifolds, Invent. Math. 85 (1986), no. 3, 637–652.
Mathematical Reviews (MathSciNet): MR87j:53061
Zentralblatt MATH: 0603.53025
Digital Object Identifier: doi:10.1007/BF01390331
[Gr1] M. Gromov, Almost flat manifolds, J. Differential Geom. 13 (1978), no. 2, 231–241.
Mathematical Reviews (MathSciNet): MR80h:53041
Zentralblatt MATH: 0432.53020
Project Euclid: euclid.jdg/1214434488
[Gr2] M. Gromov, Manifolds of negative curvature, J. Differential Geom. 13 (1978), no. 2, 223–230.
Mathematical Reviews (MathSciNet): MR80h:53040
Zentralblatt MATH: 0433.53028
Project Euclid: euclid.jdg/1214434487
[Gr3] M. Gromov, Volume and bounded cohomology, Inst. Hautes Études Sci. Publ. Math. (1982), no. 56, 5–99 (1983).
Mathematical Reviews (MathSciNet): MR84h:53053
Zentralblatt MATH: 0516.53046
[Gro] K. Grove, Metric and topological measurements of manifolds, Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990), Math. Soc. Japan, Tokyo, 1991, pp. 511–519.
Mathematical Reviews (MathSciNet): MR93c:53030
Zentralblatt MATH: 0749.53024
[GPW]1 K. Grove, P. Petersen, and J.-Y. Wu, Geometric finiteness theorems via controlled topology, Invent. Math. 99 (1990), no. 1, 205–213.
Mathematical Reviews (MathSciNet): MR90k:53075
Zentralblatt MATH: 0747.53033
Digital Object Identifier: doi:10.1007/BF01234417
[GPW]2 K. Grove, P. Petersen, and J.-Y. Wu, Erratum: “Geometric finiteness theorems via controlled topology”, Invent. Math. 104 (1991), no. 1, 221–222.
Mathematical Reviews (MathSciNet): MR92b:53065
Zentralblatt MATH: 0778.53034
Digital Object Identifier: doi:10.1007/BF01245073
[Ha] R. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982), no. 2, 255–306.
Mathematical Reviews (MathSciNet): MR84a:53050
Zentralblatt MATH: 0504.53034
Project Euclid: euclid.jdg/1214436922
[Ko] S. Kobayashi, Transformation groups in differential geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 70, Springer-Verlag, New York, 1972.
Mathematical Reviews (MathSciNet): MR50:8360
Zentralblatt MATH: 0246.53031
[Lo] J. Lohkamp, Metrics of negative Ricci curvature, Ann. of Math. (2) 140 (1994), no. 3, 655–683.
Mathematical Reviews (MathSciNet): MR95i:53042
Zentralblatt MATH: 0824.53033
Digital Object Identifier: doi:10.2307/2118620
JSTOR: links.jstor.org
[Mi] M. Min-Oo, Almost Einstein manifolds of negative Ricci curvature, J. Differential Geom. 32 (1990), no. 2, 457–472.
Mathematical Reviews (MathSciNet): MR91g:53047
Zentralblatt MATH: 0725.53050
Project Euclid: euclid.jdg/1214445315
[MR] M. Min-Oo and E. Ruh, $L\sp 2$-curvature pinching, Comment. Math. Helv. 65 (1990), no. 1, 36–51.
Mathematical Reviews (MathSciNet): MR91d:53060
Zentralblatt MATH: 0704.53031
Digital Object Identifier: doi:10.1007/BF02566591
[Pe] G. Perel'man, A. D. Aleksandrov spaces with curvatures bounded below, II, preprint.
[PWY] P. Petersen, G. Wei, and R. Ye, Controlled geometry via smoothing, preprint, 1995.
[Ro1] X. Rong, Bounding homotopy and homology groups by curvature and diameter, Duke Math. J. 78 (1995), no. 2, 427–435.
Mathematical Reviews (MathSciNet): MR96g:53054
Zentralblatt MATH: 0844.57024
Digital Object Identifier: doi:10.1215/S0012-7094-95-07820-X
Project Euclid: euclid.dmj/1077285755
[Ro2] X. Rong, On the fundamental groups of manifolds of positive sectional curvature, Ann. of Math. (2) 143 (1996), no. 2, 397–411.
Mathematical Reviews (MathSciNet): MR97a:53067
Zentralblatt MATH: 0974.53029
Digital Object Identifier: doi:10.2307/2118648
JSTOR: links.jstor.org
[Sh] Z. Shen, Deforming metrics with curvature and injectivity radius bounded from below, Arch. Math. (Basel) 62 (1994), no. 4, 354–367.
Mathematical Reviews (MathSciNet): MR95a:53056
Zentralblatt MATH: 0794.53013
Digital Object Identifier: doi:10.1007/BF01201790
[Shi] W.-X. Shi, Deforming the metric on complete Riemannian manifolds, J. Differential Geom. 30 (1989), no. 1, 223–301.
Mathematical Reviews (MathSciNet): MR90i:58202
Zentralblatt MATH: 0676.53044
Project Euclid: euclid.jdg/1214443292
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