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

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- by Herng Yi Cheng PDF
- Trans. Amer. Math. Soc.
**375**(2022), 5217-5237

## Abstract:

This paper proves that in any closed Riemannian surface $M$ with diameter $d$, the length of the $k$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 [J. Differential Geom. 89 (2011), pp. 217–232; J. Topol. Anal. 5 (2013), pp. 409–438].## References

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## Additional Information

**Herng Yi Cheng**- Affiliation: Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, Ontario M5S 2E4, Canada
- MR Author ID: 1164868
- ORCID: 0000-0001-5466-6930
- Email: herngyi@math.toronto.edu
- Received by editor(s): August 31, 2021
- Received by editor(s) in revised form: January 16, 2022
- Published electronically: April 26, 2022
- Additional Notes: This research was partially supported by the Vivekananda Graduate Scholarship from the Department of Mathematics at the University of Toronto.
- © Copyright 2022 Herng Yi Cheng
- Journal: Trans. Amer. Math. Soc.
**375**(2022), 5217-5237 - MSC (2020): Primary 53C22, 53C23
- DOI: https://doi.org/10.1090/tran/8653
- MathSciNet review: 4439503