Length of closed geodesics on Riemannian manifolds with good covers

Zhifei Zhu

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arXiv · 2412.01161

Length of closed geodesics on Riemannian manifolds with good covers

Zhifei Zhu

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Abstract

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 $N$.

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Zhifei Zhu. 2024-12-02. Length of closed geodesics on Riemannian manifolds with good covers. https://arxiv.org/abs/2412.01161

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