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ISRN Geometry
Volume 2011 (2011), Article ID 502814, 7 pages
doi:10.5402/2011/502814
Research Article
A Restriction for Singularities on Collapsing Orbifolds
Department of Mathematics and Statistics, California State University, Long Beach, CA 90840, USA
Received 8 August 2011; Accepted 5 September 2011
Academic Editors: S. Kar, U. Lindström, and E. H. Saidi
Copyright © 2011 Yu Ding. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Linked References
- W. Thurston, The Geometry and Topology of 3-Manifolds, Princeton University, 1979.
- J. Cheeger and M. Gromov, βCollapsing Riemannian manifolds while keeping their curvature bounded. II,β Journal of Differential Geometry, vol. 32, no. 1, pp. 269β298, 1990. View at Zentralblatt MATH
- J. A. Wolf, Spaces of Constant Curvature, AMS Chelsea Publishing, Providence, RI, USA, 6th edition, 2011.
- W. P. Thurston, Three-Dimensional Geometry and Topology. Vol. 1, vol. 35, Princeton University Press, Princeton, NJ, USA, 1997.
- Y. Ding, βF-structure on collapsed orbifolds,β http://www.csulb.edu/~yding/orbifold.pdf.
- J. Cheeger, K. Fukaya, and M. Gromov, βNilpotent structures and invariant metrics on collapsed manifolds,β Journal of the American Mathematical Society, vol. 5, no. 2, pp. 327β372, 1992. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
- J. Cheeger and M. Gromov, βCollapsing Riemannian manifolds while keeping their curvature bounded—I,β Journal of Differential Geometry, vol. 23, no. 3, pp. 309β346, 1986. View at Zentralblatt MATH
- M. Gromov, βAlmost flat manifolds,β Journal of Differential Geometry, vol. 13, no. 2, pp. 231β241, 1978. View at Zentralblatt MATH
- E. A. Ruh, βAlmost flat manifolds,β Journal of Differential Geometry, vol. 17, no. 1, pp. 1β14, 1982. View at Zentralblatt MATH
- P. Ghanaat, βDiskrete Gruppen und die Geometrie der Repèrebündel,β Journal für die Reine und Angewandte Mathematik, vol. 492, pp. 135β178, 1997. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
- P. Buser and Karcher, βGromov’s Almost Flat Manifolds,β Astérisque, vol. 81, 1981.
- P. Ghanaat, βAlmost Lie groups of type ,β Journal für die Reine und Angewandte Mathematik, vol. 401, pp. 60β81, 1989. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
- X. X. Chen and G. Tian, βRicci flow on Kähler-Einstein manifolds,β Duke Mathematical Journal, vol. 131, no. 1, pp. 17β73, 2006. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
- M. T. Anderson, βA survey of Einstein metrics on 4-manifolds,β in Handbook of Geometric Analysis, No. 3, vol. 14, pp. 1β39, International Press, Somerville, Mass, USA, 2010. View at Zentralblatt MATH
- K. Fukaya, βA boundary of the set of the Riemannian manifolds with bounded curvatures and diameters,β Journal of Differential Geometry, vol. 28, no. 1, pp. 1β21, 1988. View at Zentralblatt MATH