24 citations · 143 across the 29 of their papers we have counts for
37 papers
A short proof of Ball's plank theorem
Arseniy Akopyan, Alexander Polyanskii
We give a short proof of the following theorem of K. Ball: If a centrally symmetric convex body is covered by finitely many planks, then the sum of their rel…
On the total perimeter of disjoint convex bodies
Arseniy Akopyan, Alexey Glazyrin
In this note we introduce a pseudometric on convex planar curves based on distances between normal lines and show its basic properties. Then we use this pseudometric to give a shor…
Calculated Boldness: Optimizing Financial Decisions with Illiquid Assets
Stanislav Shalunov, Alexei Kitaev, Yakov Shalunov +1
We consider games of chance played by someone with external capital that cannot be applied to the game and determine how this affects risk-adjusted optimal betting. Specifically, w…
The Beauty of Random Polytopes Inscribed in the 2-sphere
Arseniy Akopyan, Herbert Edelsbrunner, Anton Nikitenko
Consider a random set of points on the unit sphere in , which can be either uniformly sampled or a Poisson point process. Its convex hull is a random inscribed polyto…
Billiards in ellipses revisited
Arseniy Akopyan, Richard Schwartz, Serge Tabachnikov
We prove some recent experimental observations of D. Reznik concerning periodic billiard orbits in ellipses. For example, the sum of cosines of the angles of a periodic billiard po…
When different norms lead to same billiard trajectories?
Arseniy Akopyan, Roman Karasev
In this paper, extending the works of Milena Radnović and Serge Tabachnikov, we establish conditions for two different non-symmetric norms to define the same billiard reflection la…