The conformal geometry of billiards

DeMarco, Laura

doi:10.1090/S0273-0979-2010-01322-7

The conformal geometry of billiards

Author: Laura DeMarco
Journal: Bull. Amer. Math. Soc. 48 (2011), 33-52
MSC (2010): Primary 37D50, 32G15
DOI: https://doi.org/10.1090/S0273-0979-2010-01322-7
Published electronically: October 15, 2010
MathSciNet review: 2738905
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Abstract: This article provides an introduction to some recent results in billiard dynamics. We present results that follow from a study of compact Riemann surfaces (equipped with a holomorphic 1-form) and an $\mathrm {SL}_2\mathbb {R}$ action on the moduli spaces of these surfaces. We concentrate on the progress toward classification of “optimal” billiard tables, those with the simplest trajectory structure.

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