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arXiv · 1909.09274

Minimizing closed geodesics on polygons and disks

Ian Adelstein·Arthur Azvolinsky·Joshua Hinman·Alexander Schlesinger
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Abstract

In this paper we study 1/k geodesics, those closed geodesics that minimize on all subintervals of length $L/k$, where $L$ is the length of the geodesic. We develop new techniques to study the minimizing properties of these curves on doubled polygons, and demonstrate a sequence of doubled polygons whose closed geodesics exhibit unbounded minimizing properties. We also compute the length of the shortest closed geodesic on doubled odd-gons and show that this length approaches 4 times the diameter.

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Ian Adelstein, Arthur Azvolinsky, Joshua Hinman, Alexander Schlesinger. 2019-09-20. Minimizing closed geodesics on polygons and disks. https://doi.org/10.2140/involve.2021.14.11

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