Nikolai Nikolov

activity

20242026

collaborators

8 papers

math.CO2026

Lattice coverings by parallelotopes containing cube vertices

Dragomir Grozev, Nikolai Nikolov

We investigate when a parallelotope containing vertices of the unit cube $Q_{n} = [0, 1]^{n}$ covers $R^{n}$ by integer translates. We prove the covering property for every parallelepi…

math.MG2026

Maximal volumes of pyramids in the unit cube

Nikolai Nikolov

Let $Q_{n} = [0, 1]^{n}$ , $n \geq 2$ . Denote by $M_{n}$ be the maximal volume of a pyramid in $Q_{n}$ whose base is a hyperplane section of $Q_{n}$ , and by $M_{n}^{0}$ the corresponding maximum when t…

math.CV2026

A Note on the Converse Sendov Problem

Dragomir Grozev, Nikolai Nikolov

For a polynomial of degree $n$ whose zeros lie in the closed unit disk, we determine the largest possible distance from a prescribed critical point of modulus $r$ to the nearest ze…

math.MG2026

Geometric optimization problems generated by plane curves

Petar Kenderov, Oleg Mushkarov, Nikolai Nikolov

Let $γ_{1}$ and $γ_{2}$ be regular $C^{1}$ -smooth curves in the plane and $γ$ be a regular $C^{2}$ -smooth curve in the same plane. Consider all triples of points $(A, A_{1}, A_{2})$ , $A \in γ$ …

math.MG2026

Moving rectangular sofas in planar and spatial corridors

Oleg Mushkarov, Nikolai Nikolov

We consider eight natural planar corridors, including the standard $L$ -shaped one, and characterize the rectangles that can move around their corners. As a bi-product we d…

math.MG2025

A Generalization of a Classical Geometric Extremum Problem

Petar Kenderov, Oleg Mushkarov, Nikolai Nikolov

Let $\partial C$ be the boundary of a compact convex body $C$ in $R^{n}, n \geq 2$ , and $O$ be an interior point of $C$ . Every straight line…

math.MG2025

On a geometric extremum problem for convex cones

Oleg Mushkarov, Nikolai Nikolov

We discuss the optimization problem for minimizing the $(n - 1)$ -volume of the intersection of a convex cone $K$ in $R^{n}$ with a hyperplane through a given point, first consider…

math.CV2024

A Picard little theorem for entire functions of matrices

Oleg Mushkarov, Nikolai Nikolov

An analog of Picard's little theorem for entire functions of matrices is proved.