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Precompactness of solutions to the Ricci flow in the absence of injectivity radius estimates

David Glickenstein

Geometry & Topology 7 (2003) 487–510
Bibliography
1 D Burago, Y Burago, S Ivanov, A course in metric geometry, Graduate Studies in Mathematics 33, American Mathematical Society (2001) MR1835418
2 M Carfora, J Isenberg, M Jackson, Convergence of the Ricci flow for metrics with indefinite Ricci curvature, J. Differential Geom. 31 (1990) 249 MR1030672
3 M Carfora, A Marzuoli, Model geometries in the space of Riemannian structures and Hamilton's flow, Classical Quantum Gravity 5 (1988) 659 MR940055
4 J Cheeger, K Fukaya, M Gromov, Nilpotent structures and invariant metrics on collapsed manifolds, J. Amer. Math. Soc. 5 (1992) 327 MR1126118
5 J Cheeger, M Gromov, Collapsing Riemannian manifolds while keeping their curvature bounded I, J. Differential Geom. 23 (1986) 309 MR852159
6 J Cheeger, M Gromov, Collapsing Riemannian manifolds while keeping their curvature bounded II, J. Differential Geom. 32 (1990) 269 MR1064875
7 J Cheeger, M Gromov, M Taylor, Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds, J. Differential Geom. 17 (1982) 15 MR658471
8 J Cheeger, X Rong, Collapsed Riemannian manifolds with bounded diameter and bounded covering geometry, Geom. Funct. Anal. 5 (1995) 141 MR1334865
9 S Y Cheng, P Li, S T Yau, On the upper estimate of the heat kernel of a complete Riemannian manifold, Amer. J. Math. 103 (1981) 1021 MR630777
10 B Chow, D Glickenstein, P Lu, Collapsing sequences of solutions to the Ricci flow on 3–manifolds with almost nonnegative curvature, arXiv:math.DG/0305228
11 B Chow, D Knopf, P Lu, Hamilton's injectivity radius estimate for sequences with almost nonnegative curvature operators, Comm. Anal. Geom. 10 (2002) 1151 MR1957666
12 K Fukaya, Theory of convergence for Riemannian orbifolds, Japan. J. Math. $($N.S.$)$ 12 (1986) 121 MR914311
13 K Fukaya, Collapsing Riemannian manifolds to ones of lower dimensions, J. Differential Geom. 25 (1987) 139 MR873459
14 K Fukaya, A boundary of the set of the Riemannian manifolds with bounded curvatures and diameters, J. Differential Geom. 28 (1988) 1 MR950552
15 K Fukaya, Collapsing Riemannian manifolds to ones with lower dimension II, J. Math. Soc. Japan 41 (1989) 333 MR984756
16 D Glickenstein, Precompactness of solutions to the Ricci flow and a maximum principle for combinatorial Yamabe flow, PhD thesis, University of California at San Diego (2003)
17 R E Greene, H Wu, Lipschitz convergence of Riemannian manifolds, Pacific J. Math. 131 (1988) 119 MR917868
18 M Gromov, Metric structures for Riemannian and non–Riemannian spaces, Progress in Mathematics 152, Birkhäuser (1999) MR1699320
19 R S Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982) 255 MR664497
20 R S Hamilton, The Ricci flow on surfaces, from: "Mathematics and general relativity (Santa Cruz, CA, 1986)", Contemp. Math. 71, Amer. Math. Soc. (1988) 237 MR954419
21 R S Hamilton, A compactness property for solutions of the Ricci flow, Amer. J. Math. 117 (1995) 545 MR1333936
22 R S Hamilton, The formation of singularities in the Ricci flow, from: "Surveys in differential geometry, Vol. II (Cambridge, MA, 1993)", Int. Press, Cambridge, MA (1995) 7 MR1375255
23 R Hamilton, J Isenberg, Quasi-convergence of Ricci flow for a class of metrics, Comm. Anal. Geom. 1 (1993) 543 MR1266479
24 J Isenberg, M Jackson, Ricci flow of locally homogeneous geometries on closed manifolds, J. Differential Geom. 35 (1992) 723 MR1163457
25 D Knopf, Quasi-convergence of the Ricci flow, Comm. Anal. Geom. 8 (2000) 375 MR1753322
26 D Knopf, K McLeod, Quasi-convergence of model geometries under the Ricci flow, Comm. Anal. Geom. 9 (2001) 879 MR1868923
27 P Lu, A compactness property for solutions of the Ricci flow on orbifolds, Amer. J. Math. 123 (2001) 1103 MR1867313
28 G Perelman, The entropy formula for the Ricci flow and its geometric applications, arXiv:math.DG/0211159
29 G Perelman, The Ricci flow with surgery on three-manifolds, arXiv:math.DG/0303109
30 S Peters, Convergence of Riemannian manifolds, Compositio Math. 62 (1987) 3 MR892147
31 P Petersen, Convergence theorems in Riemannian geometry, from: "Comparison geometry (Berkeley, CA, 1993–94)", Math. Sci. Res. Inst. Publ. 30, Cambridge Univ. Press (1997) 167 MR1452874
32 A Petrunin, X Rong, W Tuschmann, Collapsing vs. positive pinching, Geom. Funct. Anal. 9 (1999) 699 MR1719598
33 L S Pontryagin, Topological groups, Translated from the second Russian edition by Arlen Brown, Gordon and Breach Science Publishers (1966) MR0201557
34 X Rong, Collapsed manifolds with pinched positive sectional curvature, J. Differential Geom. 51 (1999) 335 MR1728302
35 T Shioya, T Yamaguchi, Collapsing three-manifolds under a lower curvature bound, J. Differential Geom. 56 (2000) 1 MR1863020
36 T Yamaguchi, Collapsing and pinching under a lower curvature bound, Ann. of Math. $(2)$ 133 (1991) 317 MR1097241