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| Main Author: | |
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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2009.00226 |
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Table of Contents:
- Let $M$ be an open $n$-manifold of nonnegative Ricci curvature and let $p\in M$. We show that if $(M,p)$ has escape rate less than some positive constant $ε(n)$, that is, minimal representing geodesic loops of $π_1(M,p)$ escape from any bounded balls at a small linear rate with respect to their lengths, then $π_1(M,p)$ is virtually abelian. This generalizes the author's previous work, where the zero escape rate is considered.