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arXiv · 2109.00438

Curvature-free linear length bounds on geodesics in closed Riemannian surfaces

Herng Yi Cheng
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Abstract

This paper proves that in any closed Riemannian surface $M$ with diameter $d$, the length of the $k^\text{th}$-shortest geodesic between two given points $p$ and $q$ is at most $8kd$. This bound can be tightened further to $6kd$ if $p = q$. This improves prior estimates by A. Nabutovsky and R. Rotman.

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Herng Yi Cheng. 2021-09-01. Curvature-free linear length bounds on geodesics in closed Riemannian surfaces. https://doi.org/10.1090/tran/8653

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