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Equality cases in Viterbo's conjecture and isoperimetric billiard inequalities

- Alexey Balitskiy
- Mathematics
- 5 December 2015

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 the product of a… Expand

Elementary approach to closed billiard trajectories in asymmetric normed spaces

- A. Akopyan, Alexey Balitskiy, R. Karasev, A. Sharipova
- Mathematics
- 2 January 2014

We apply the technique of K\'aroly Bezdek and Daniel Bezdek to study billiard trajectories in convex bodies, when the length is measured with a (possibly asymmetric) norm. We prove a lower bound for… Expand

A multi-plank generalization of the Bang and Kadets inequalities

- Alexey Balitskiy
- MathematicsIsrael Journal of Mathematics
- 14 March 2020

If a convex body in $\mathbb{R}^n$ is covered by the union of convex bodies, multiple subadditivity questions can be asked. The subadditivity of the width is the subject of the celebrated plank… Expand

On the Circle Covering Theorem by A.W. Goodman and R.E. Goodman

- A. Akopyan, Alexey Balitskiy, M. Grigorev
- Mathematics, Computer ScienceDiscret. Comput. Geom.
- 13 May 2016

TLDR

On the Circle Covering Theorem by A .

- Alexey Balitskiy, M. Grigorev
- 2017

In 1945, A.W. Goodman and R.E. Goodman proved the following conjecture by P. Erdős: Given a family of (round) disks of radii r1, . . ., rn in the plane, it is always possible to cover them by a disk… Expand

Flip cycles in plabic graphs

- Alexey Balitskiy, Julian Wellman
- Mathematics
- 5 February 2019

Planar bicolored (plabic) graphs are combinatorial objects introduced by Postnikov to give parameterizations of the positroid cells of the totally nonnegative Grassmannian $$\text {Gr}^{\ge 0}(n,k)$$… Expand

Another Ham Sandwich in the Plane

- Alexey Balitskiy, Alexey Garber, R. Karasev
- Mathematics
- 29 July 2013

We show that every two nice measures in the plane can be partitioned into equal halves by translation of an angle from any k-fan when k is odd and in some cases when k is even. We also give some… Expand

Equality cases in Viterbo's conjecture related to permutohedra

- Alexey Balitskiy
- Mathematics
- 5 December 2015

In this note we show, using the billiard technique, that the product of a regular permutohedron and a regular simplex delivers an equality in Viterbo's conjecture.

Optimality of codes with respect to error probability in Gaussian noise

- Alexey Balitskiy, R. Karasev, Alexander Tsigler
- Mathematics, Computer ScienceArXiv
- 27 January 2017

TLDR

Geometric Complexity of Planar Drawings

- Jiwon Choi, Alexey Balitskiy
- 2018

We say that a planar drawing of a graph is 1-thick if the distance between the images of any two vertices, a vertex and an edge, and two non-adjacent edges is at least 1. We prove that the cylinder… Expand

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