|
|||||
 |
|
|
|
|
|
|
|
Minimizing
closed geodesics on polygons and disks
Ian Adelstein, Arthur Azvolinsky, Joshua Hinman and Alexander Schlesinger
Vol. 14 (2021), No. 1, 11–52
|
Abstract |
|
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. |
PDF Access Denied
We have not been able to recognize your IP address
18.218.48.62
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for USD 30.00:
Keywords
closed geodesics, regular polygons, billiards
|
Mathematical Subject Classification 2010
Primary: 53C22
|
Milestones
Received: 19 September 2019
Revised: 11 May 2020
Accepted: 5 July 2020
Published: 4 March 2021
Communicated by Frank Morgan
|
Authors |
| Ian Adelstein | |
| Department of Mathematics Yale University New Haven, CT United States |
|
| Arthur Azvolinsky | |
| Department of Mathematics Yale University New Haven, CT United States |
|
| Joshua Hinman | |
| Department of Mathematics Yale University New Haven, CT United States |
|
| Alexander Schlesinger | |
| Department of Mathematics Yale University New Haven, CT United States |
|
