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2021 On the escape rate of geodesic loops in an open manifold with nonnegative Ricci curvature
Jiayin Pan
Geom. Topol. 25(2): 1059-1085 (2021). DOI: 10.2140/gt.2021.25.1059

Abstract

A consequence of the Cheeger–Gromoll splitting theorem states that for any open manifold (M,x) of nonnegative Ricci curvature, if all the minimal geodesic loops at x that represent elements of π1(M,x) are contained in a bounded ball, then π1(M,x) is virtually abelian. We generalize the above result: if these minimal representing geodesic loops of π1(M,x) escape from any bounded metric balls at a sublinear rate with respect to their lengths, then π1(M,x) is virtually abelian.

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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

Information

Received: 6 March 2020; Revised: 17 May 2020; Accepted: 17 June 2020; Published: 2021
First available in Project Euclid: 28 May 2021

Digital Object Identifier: 10.2140/gt.2021.25.1059

Subjects:
Primary: 53C20 , 53C23
Secondary: 53C21 , 57S30

Keywords: fundamental groups , Ricci curvature

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.25 • No. 2 • 2021
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