Length of closed geodesics on Riemannian manifolds with good covers

2024/12/02 by Zhifei Zhu, Zhu, Zhifei
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Morphological variations and asymmetry #Advanced Differential Geometry Research

paper · pdf · doi:10.48550/arxiv.2412.01161

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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