We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham Research Online
You are in:

Minimizing length of billiard trajectories in hyperbolic polygons.

Parker, John R. and Peyerimhoff, Norbert and Siburg, Karl Friedrich (2018) 'Minimizing length of billiard trajectories in hyperbolic polygons.', Conformal geometry and dynamics., 22 . pp. 315-332.


Closed billiard trajectories in a polygon in the hyperbolic plane can be coded by the order in which they hit the sides of the polygon. In this paper, we consider the average length of cyclically related closed billiard trajectories in ideal hyperbolic polygons and prove the conjecture that this average length is minimized for regular hyperbolic polygons. The proof uses a strict convexity property of the geodesic length function in Teichmüller space with respect to the Weil-Petersson metric, a fundamental result established by Wolpert.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
Download PDF
Publisher Web site:
Publisher statement:Accepted manuscript available under a CC-BY-NC-ND licence.
Date accepted:29 October 2018
Date deposited:31 October 2018
Date of first online publication:07 December 2018
Date first made open access:No date available

Save or Share this output

Look up in GoogleScholar