16 citations · 37 across the 11 of their papers we have counts for
12 papers · 1 filter
Systolic inequalities for the number of vertices
Sergey Avvakumov, Alexey Balitskiy, Alfredo Hubard +1
Inspired by the classical Riemannian systolic inequality of Gromov we present a combinatorial analogue providing a lower bound on the number of vertices of a simplicial complex in…
Waist of maps measured via Urysohn width
Alexey Balitskiy, Aleksandr Berdnikov
We discuss various questions of the following kind: for a continuous map from a compact metric space to a simplicial complex, can one guarantee the existence of a fiber l…
Local-to-global Urysohn width estimates
Alexey Balitskiy, Aleksandr Berdnikov
The notion of the Urysohn -width measures to what extent a metric space can be approximated by a -dimensional simplicial complex. We investigate how local Urysohn width bound…
A multi-plank generalization of the Bang and Kadets inequalities
Alexey Balitskiy
If a convex body is covered by the union of convex bodies , multiple subadditivity questions can be asked. Two classical results regard t…
Optimality of codes with respect to error probability in Gaussian noise
Alexey Balitskiy, Roman Karasev, Alexander Tsigler
We consider geometrical optimization problems related to optimizing the error probability in the presence of a Gaussian noise. One famous questions in the field is the "weak simple…
On the Circle Covering Theorem by A. W. Goodman and R. E. Goodman
Arseniy Akopyan, Alexey Balitskiy, Mikhail Grigorev
In 1945, A. W. Goodman and R. E. Goodman proved the following conjecture by P. Erdős: Given a family of (round) disks of radii , , in the plane it is always poss…
Dependence of the heavily covered point on parameters
Alexey Balitskiy, Roman Karasev
We examine Gromov's method of selecting a point "heavily covered" by simplices formed by a given finite point sets, in order to understand the dependence of the heavily covered poi…
Equality cases in Viterbo's conjecture and isoperimetric billiard inequalities
Alexey Balitskiy
In this note we apply the billiard technique to deduce some results on Viterbo's conjectured inequality between volume of a convex body and its symplectic capacity. We show that th…
Billiards in convex bodies with acute angles
Arseniy Akopyan, Alexey Balitskiy
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 ha…
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…
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…
Another ham sandwich in the plane
Alexey Balitskiy, Alexey Garber, Roman Karasev
We show that every two nice measures in the plane can be partitioned into equal halves by translation of an angle from arbitrary k-fan when k is odd and in some cases when k is eve…