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5 papers · 2 filters
The Tammes problem for N=14
Oleg R. Musin, Alexey S. Tarasov
The Tammes problem is to find the arrangement of N points on a unit sphere which maximizes the minimum distance between any two points. This problem is presently solved for several…
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…
Bang's problem and symplectic invariants
Arseniy Akopyan, Roman Karasev, Fedor Petrov
We consider the Tarski--Bang problem about covering of convex bodies by planks. The results of this kind give a lower bound on the sum of widths of planks (regions between a pair o…
Bounds for Pach's selection theorem and for the minimum solid angle in a simplex
Roman Karasev, Jan Kynčl, Pavel Paták +2
We estimate the selection constant in the following geometric selection theorem by Pach: For every positive integer there is a constant such that whenever $X_1,..., X…
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…