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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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Additional Information

Laura DeMarco
Affiliation: Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago
Email: demarco@math.uic.edu

DOI: https://doi.org/10.1090/S0273-0979-2010-01322-7
Received by editor(s): July 19, 2010
Published electronically: October 15, 2010
Article copyright: © Copyright 2010 American Mathematical Society

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