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| Format: | Preprint |
| Veröffentlicht: |
2020
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2009.00226 |
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| _version_ | 1866915365655674880 |
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| author | Pan, Jiayin |
| author_facet | Pan, Jiayin |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_00226 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Nonnegative Ricci curvature and escape rate gap Pan, Jiayin Differential Geometry 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. |
| title | Nonnegative Ricci curvature and escape rate gap |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2009.00226 |