Nikolai Nikolov

collaborators

5 papers

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

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.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.CV2025

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.