Nonnegative Ricci curvature and escape rate gap

References

[1] J. Cheeger and T. H. Colding, Lower bounds on Ricci curvature and the almost rigidity of warped products, Ann. of Math. (2) 144 (1996), no. 1, 189–237. 10.2307/2118589Search in Google Scholar

[2] J. Cheeger and T. H. Colding, On the structure of spaces with Ricci curvature bounded below. II, J. Differential Geom. 54 (2000), no. 1, 13–35. 10.4310/jdg/1214342145Search in Google Scholar

[3] J. Cheeger and D. Gromoll, The splitting theorem for manifolds of nonnegative Ricci curvature, J. Differential Geom. 6 (1971/72), 119–128. 10.4310/jdg/1214430220Search in Google Scholar

[4] J. Cheeger and D. Gromoll, On the structure of complete manifolds of nonnegative curvature, Ann. of Math. (2) 96 (1972), 413–443. 10.2307/1970819Search in Google Scholar

[5] T. H. Colding and A. Naber, Sharp Hölder continuity of tangent cones for spaces with a lower Ricci curvature bound and applications, Ann. of Math. (2) 176 (2012), no. 2, 1173–1229. 10.4007/annals.2012.176.2.10Search in Google Scholar

[6] K. Fukaya and T. Yamaguchi, The fundamental groups of almost non-negatively curved manifolds, Ann. of Math. (2) 136 (1992), no. 2, 253–333. 10.2307/2946606Search in Google Scholar

[7] M. Gromov, Groups of polynomial growth and expanding maps, Publ. Math. Inst. Hautes Études Sci. 53 (1981), 53–73. 10.1007/BF02698687Search in Google Scholar

[8] V. Kapovitch and B. Wilking, Structure of fundamental groups of manifolds of Ricci curvature bounded below, preprint (2011), https://arxiv.org/abs/1105.5955. Search in Google Scholar

[9] J. Milnor, A note on curvature and fundamental group, J. Differential Geom. 2 (1968), 1–7. 10.4310/jdg/1214501132Search in Google Scholar

[10] J. Pan, Nonnegative Ricci curvature, almost stability at infinity, and structure generation of fundamental groups, preprint (2018), https://arxiv.org/abs/1809.10220. Search in Google Scholar

[11] J. Pan, Nonnegative Ricci curvature, stability at infinity, and finite generation of fundamental groups, Geom. Topol. 23 (2019), no. 6, 3203–3231. 10.2140/gt.2019.23.3203Search in Google Scholar

[12] J. Pan, On the escape rate of geodesic loops in an open manifold with nonnegative Ricci curvature, Geom. Topol. 25 (2021), no. 2, 1059–1085. 10.2140/gt.2021.25.1059Search in Google Scholar

[13] C. Sormani and G. Wei, Various covering spectra for complete metric spaces, Asian J. Math. 19 (2015), no. 1, 171–202. 10.4310/AJM.2015.v19.n1.a7Search in Google Scholar

[14] G. Wei, Examples of complete manifolds of positive Ricci curvature with nilpotent isometry groups, Bull. Amer. Math. Soc. (N. S.) 19 (1988), no. 1, 311–313. 10.1090/S0273-0979-1988-15653-4Search in Google Scholar

[15] B. Wilking, On fundamental groups of manifolds of nonnegative curvature, Differential Geom. Appl. 13 (2000), no. 2, 129–165. 10.1016/S0926-2245(00)00030-9Search in Google Scholar