Vol. 12, No. 7, 2019

 Recent Issues
 The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1944-4184 (e-only) ISSN: 1944-4176 (print) Author Index Coming Soon Other MSP Journals
Closed geodesics on doubled polygons

Vol. 12 (2019), No. 7, 1219–1227
Abstract

We study $1∕k$-geodesics, those closed geodesics that minimize on any subinterval of length $L∕k$, where $L$ is the length of the geodesic. We investigate the existence and behavior of these curves on doubled polygons and show that every doubled regular $n$-gon admits a $1∕\left(2n\right)$-geodesic. For the doubled regular $p$-gons, with $p$ an odd prime, we conjecture that $k=2p$ is the minimum value for $k$ such that the space admits a $1∕k$-geodesic.

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/involve

We have not been able to recognize your IP address 34.232.51.240 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

or by using our contact form.

Keywords
closed geodesics, regular polygons, billiard paths
Mathematical Subject Classification 2010
Primary: 53C20, 53C22