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Minimizing
closed geodesics on polygons and disks
Ian Adelstein, Arthur Azvolinsky, Joshua Hinman and Alexander Schlesinger
Vol. 14 (2021), No. 1, 11–52
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Abstract |
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We study -geodesics, those closed geodesics that minimize on all subintervals of length , where 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 where the minimizing index (the smallest such that the space admits a -geodesic) is unbounded. We also compute the length of the shortest closed geodesic on doubled odd-gons and show that this length approaches diameter. |
Keywords
closed geodesics, regular polygons, billiards
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Mathematical Subject Classification 2010
Primary: 53C22
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Milestones
Received: 19 September 2019
Revised: 11 May 2020
Accepted: 5 July 2020
Published: 4 March 2021
Communicated by Frank Morgan
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Authors |
| Ian Adelstein | |
| Department of Mathematics Yale University New Haven, CT United States |
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| Arthur Azvolinsky | |
| Department of Mathematics Yale University New Haven, CT United States |
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| Joshua Hinman | |
| Department of Mathematics Yale University New Haven, CT United States |
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| Alexander Schlesinger | |
| Department of Mathematics Yale University New Haven, CT United States |
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