16 citations · 37 across the 11 of their papers we have counts for
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math.MG2014★ 6 cited
Shortest Closed Billiard Trajectories in the Plane and Equality Cases in Mahler's Conjecture
Alexey Balitskiy
In this note we prove some Rogers-Shepard type inequalities for the lengths of shortest closed billiard trajectories, mostly in the planar case. We also establish some properties o…
math.MG2014★ 16 cited
Elementary approach to closed billiard trajectories in asymmetric normed spaces
Arseniy V. Akopyan, Alexey M. Balitskiy, Roman N. Karasev +1
We apply the technique of Károly Bezdek and Daniel Bezdek to study billiard trajectories in convex bodies, when the length is measured with a (possibly asymmetric) norm. We prove a…