Nikolai Nikolov

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20242026

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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.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…