Abstract
In this paper we investigate the existence of closed billiard trajectories in not necessarily smooth convex bodies. In particular, we show that if a body K ⊂ Rd has the property that the tangent cone of every non-smooth point q ∉ ∂K is acute (in a certain sense), then there is a closed billiard trajectory in K.
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Supported by People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement n°[291734].
Supported by the Russian Foundation for Basic Research grant 15-31-20403 (mol a ved), by the Russian Foundation for Basic Research grant 15-01-99563 A, in part by the Moebius Contest Foundation for Young Scientists, and in part by the Simons Foundation.
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Akopyan, A., Balitskiy, A. Billiards in convex bodies with acute angles. Isr. J. Math. 216, 833–845 (2016). https://doi.org/10.1007/s11856-016-1429-z
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DOI: https://doi.org/10.1007/s11856-016-1429-z