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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.

Abstract

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.
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1090/ecgd/328
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

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