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

Author:
Herng Yi Cheng

Journal:
Trans. Amer. Math. Soc.

MSC (2020):
Primary 53C22, 53C23

DOI:
https://doi.org/10.1090/tran/8653

Published electronically:
April 26, 2022

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Abstract | References | Similar Articles | Additional Information

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].

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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.

Article copyright:
© Copyright 2022
Herng Yi Cheng