Abstract
A consequence of the Cheeger–Gromoll splitting theorem states that for any open manifold of nonnegative Ricci curvature, if all the minimal geodesic loops at that represent elements of are contained in a bounded ball, then is virtually abelian. We generalize the above result: if these minimal representing geodesic loops of escape from any bounded metric balls at a sublinear rate with respect to their lengths, then is virtually abelian.
Citation
Jiayin Pan. "On the escape rate of geodesic loops in an open manifold with nonnegative Ricci curvature." Geom. Topol. 25 (2) 1059 - 1085, 2021. https://doi.org/10.2140/gt.2021.25.1059
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