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On
the escape rate of geodesic loops in an open manifold with
nonnegative Ricci curvature
Jiayin Pan |
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Geometry & Topology 25 (2021) 1059–1085
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Abstract |
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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. |
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Keywords
Ricci curvature, fundamental groups
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Mathematical Subject Classification 2010
Primary: 53C20, 53C23
Secondary: 53C21, 57S30
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References |
Publication
Received: 6 March 2020
Revised: 17 May 2020
Accepted: 17 June 2020
Published: 27 April 2021
Proposed: Tobias H Colding
Seconded: András I Stipsicz, David M Fisher
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Authors |
| Jiayin Pan | |
| Department of Mathematics University of California, Santa Barbara Santa Barbara, CA United States |
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