Collapsing Riemannian manifolds to ones with lower dimension II

Kenji FUKAYA

doi:10.2969/jmsj/04120333

Kenji FUKAYA

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1989 Volume 41 Issue 2 Pages 333-356

DOI https://doi.org/10.2969/jmsj/04120333

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Published: 1989 Received: September 18, 1987 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) J. Bemelmans, Min-Oo and E. A. Ruh, Smoothing Riemannian metrics, Math. Z., 188 (1984), 69-74.
2) J. Cheeger and M. Gromov, Collapsing Riemannian manifolds while keeping their curvatures bounded I, J. Diff. Geometry, 23 (1986), 309-346.
3) J. Cheeger and M. Gromov, Collapsing Riemannian manifolds while keeping their curvatures bounded II, preprint.
4) K. Fukaya, Theory of convergence for Riemannian orbifolds, Japanese J. Math., 12 (1986), 121-160.
5) K. Fukaya, On a compactification of the set of Riemannian manifolds with bounded curvatures and diameters, Lecture Notes in Math., 1201, Springer, 1986, pp. 89-107.
6) K. Fukaya, Collapsing of Riemannian manifolds and eigen-values of Laplace operator, Invent. Math., 87 (1987), 517-547.
7) K. Fukaya, Collapsing Riemannian manifolds to ones with lower dimension, J. Diff. Geometry, 25 (1987), 139-156.
8) K. Fukaya, A boundary of the set of the Riemannian manifolds with bounded curvatures and diameters, J. Diff. Geometry, 28 (1988), 1-21.
9) K Fukaya, A compactness theorem of a set of aspherical Riemannian orbifolds, in “A Fete of Topology” edited by Matsumoto, Mizutani and Morita, Academic Press, 1988, pp. 331-355.
10) M. Gromov, Volume and bounded cohomology, Publ. I. H. E. S., 56 (1983), 213-307.
11) M. Gromov (with J. Lafontaine and P. Pansu), Structure métrique pour les variétés riemannienne, Cedic Fernand/Nathan, 1981.
12) P. Pansu, Effondrement des variétés riemanniennes (d'aprés J. Cheeger et M. Gromov), Seminar Bourbaki, 36°, Année 1983/84, no. 618.
13) M. Raghunathan, Discrete subgroup of Lie groups, Springer, 1972.
14) E. Ruh, Almost flat manifolds, J. Diff. Geometry, 17 (1982), 1-14.

Right : [1] J. Bemelmans, Min-Oo and E. A. Ruh, Smoothing Riemannian metrics, Math. Z., 188 (1984), 69-74.
[2] J. Cheeger and M. Gromov, Collapsing Riemannian manifolds while keeping their curvatures bounded I, J. Diff. Geometry, 23 (1986), 309-346.
[3] J. Cheeger and M. Gromov, Collapsing Riemannian manifolds while keeping their curvatures bounded II, preprint.
[4] K. Fukaya, Theory of convergence for Riemannian orbifolds, Japanese J. Math., 12 (1986), 121-160.
[5] K. Fukaya, On a compactification of the set of Riemannian manifolds with bounded curvatures and diameters, Lecture Notes in Math., 1201, Springer, 1986, pp. 89-107.
[6] K. Fukaya, Collapsing of Riemannian manifolds and eigen-values of Laplace operator, Invent. Math., 87 (1987), 517-547.
[7] K. Fukaya, Collapsing Riemannian manifolds to ones with lower dimension, J. Diff. Geometry, 25 (1987), 139-156.
[8] K. Fukaya, A boundary of the set of the Riemannian manifolds with bounded curvatures and diameters, J. Diff. Geometry, 28 (1988), 1-21.
[9] K Fukaya, A compactness theorem of a set of aspherical Riemannian orbifolds, in “A Fete of Topology” edited by Matsumoto, Mizutani and Morita, Academic Press, 1988, pp. 331-355.
[10] M. Gromov, Volume and bounded cohomology, Publ. I. H. E. S., 56 (1983), 213-307.
[11] M. Gromov (with J. Lafontaine and P. Pansu), Structure métrique pour les variétés riemannienne, Cedic Fernand/Nathan, 1981.
[12] P. Pansu, Effondrement des variétés riemanniennes (d'aprés J. Cheeger et M. Gromov), Seminar Bourbaki, 36°, Année 1983/84, no. 618.
[13] M. Raghunathan, Discrete subgroup of Lie groups, Springer, 1972.
[14] E. Ruh, Almost flat manifolds, J. Diff. Geometry, 17 (1982), 1-14.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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