K. Tikhomirov

activity

20152021

most citedRandomized coverings of a convex body with its homothetic copies, and illumination

1 citations · 1 across the 6 of their papers we have counts for

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math.MG2018

On the Banach-Mazur distance to cross-polytope

Konstantin Tikhomirov

Let $n \geq 3$ , and let $B_{1}^{n}$ be the standard $n$ -dimensional cross-polytope (i.e. the convex hull of standard coordinate vectors and their negatives). We show that there exists a…

math.MG2017

Cube is a strict local maximizer for the illumination number

Galyna Livshyts, Konstantin Tikhomirov

It was conjectured by Levi, Hadwiger, Gohberg and Markus that the boundary of any convex body in $R^{n}$ can be illuminated by at most $2^{n}$ light sources, and, moreover, $…

math.MG2017

Superconcentration, and randomized Dvoretzky's theorem for spaces with 1-unconditional bases

Konstantin Tikhomirov

Let $n$ be a sufficiently large natural number and let $B$ be an origin-symmetric convex body in $R^{n}$ in the $ℓ$ -position, and such that the normed space $(R^{n}, ∥ \cdot ∥_{B})$ ad…

math.MG2016★ 1 cited

Randomized coverings of a convex body with its homothetic copies, and illumination

Galyna Livshyts, Konstantin Tikhomirov

We present a probabilistic model of illuminating a convex body by independently distributed light sources. In addition to recovering C.A. Rogers' upper bounds for the illumination…