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Licensed Unlicensed Requires Authentication Published by De Gruyter November 12, 2021

Nonnegative Ricci curvature and escape rate gap

Jiayin Pan

Abstract

Let M be an open n-manifold of nonnegative Ricci curvature and let pM. We show that if (M,p) has escape rate less than some positive constant ϵ(n), that is, minimal representing geodesic loops of π1(M,p) escape from any bounded balls at a small linear rate with respect to their lengths, then π1(M,p) is virtually abelian. This generalizes the author’s previous work [J. Pan, On the escape rate of geodesic loops in an open manifold with nonnegative Ricci curvature, Geom. Topol. 25 2021, 2, 1059–1085], where the zero escape rate is considered.

Funding statement: The author was partially supported by AMS Simons travel grant when preparing this work.

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Received: 2020-09-17
Revised: 2021-09-24
Published Online: 2021-11-12
Published in Print: 2022-01-01

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