A. Aliev

activity

20222025

collaborators

4 papers

math.MG2025

Mahler-type volume inequality for convex bodies with tetrahedral symmetry

Arkadiy Aliev

Let $K$ be a convex body in $R^{n}$ . We denote the volume of $K$ by $∣ K ∣$ , and the polar body of its difference body $K - K$ by $(K - K)^{\circ}$ . We pr…

math.MG2023

The exact bound for the reverse isodiametric problem in 3-space

Arkadiy Aliev

Let $K$ be a convex body in $R^{3}$ . We denote the volume of $K$ by $V o l (K)$ and the diameter of $K$ by $D iam (K) .$ In this paper we prove that there exists a linear biject…

math.MG2022

On the Packing Density Bound in 3-Space

Arkadiy Aliev

The note shows an easy way to improve E.H. Smith's packing density bound in $R^{3}$ from $0.53835...$ to $0.54755...$ .

math.MG2022

New estimates for $d_{2, 1}$ and $d_{3, 2}$

Arkadiy Aliev

Let $K$ be a convex body in $R^{n}$ . Let $d_{n, n - 1} (K)$ be the smallest possible density of a non-separable lattice of translates of $K$ . In this paper we prove the estim…

Mahler-type volume inequality for convex bodies with tetrahedral symmetry

The exact bound for the reverse isodiametric problem in 3-space

On the Packing Density Bound in 3-Space

New estimates for d2,1​ and d3,2​

New estimates for $d_{2, 1}$ and $d_{3, 2}$