Corpus ID: 237372347

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

@inproceedings{Cheng2021CurvaturefreeLL,
title={Curvature-free linear length bounds on geodesics in closed Riemannian surfaces},
author={Herng Yi Cheng},
year={2021}
}
• Herng Yi Cheng
• Published 1 September 2021
• Mathematics
This paper proves that in any closed Riemannian surface M with diameter d, the length of the kth-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 [19, 21].

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