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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.01161 |
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| _version_ | 1866913593715326976 |
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| author | Zhu, Zhifei |
| author_facet | Zhu, Zhifei |
| contents | In this article, we prove a generalization of our previous result in [12]. In particular, we show that for an $n$-dimensional, simply connected Riemannian manifold with diameter $D$ and volume $V$. Suppose that $M$ admits a good cover consisting of $N$ elements. Then, the length of a shortest closed geodesic on $M$ is bounded by some function that only depends on $V, D$, and $N$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_01161 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Length of closed geodesics on Riemannian manifolds with good covers Zhu, Zhifei Differential Geometry 53C22, 53C23 In this article, we prove a generalization of our previous result in [12]. In particular, we show that for an $n$-dimensional, simply connected Riemannian manifold with diameter $D$ and volume $V$. Suppose that $M$ admits a good cover consisting of $N$ elements. Then, the length of a shortest closed geodesic on $M$ is bounded by some function that only depends on $V, D$, and $N$. |
| title | Length of closed geodesics on Riemannian manifolds with good covers |
| topic | Differential Geometry 53C22, 53C23 |
| url | https://arxiv.org/abs/2412.01161 |