Vsevolod Voronov

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20242026

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math.MG2026

A counterexample to Gale's conjecture in $R^{3}$

Vsevolod Voronov

It is known that for every partition of the sphere $S^{2}$ of unit diameter into four parts, the largest diameter of a part is at least $(3 + 3) /6 = 0.88807 \dots$ , and th…

math.MG2026

Reducing the upper bound for the Borsuk number in $R^{4}$ to 8

Alexander Tolmachev, Vsevolod Voronov

The Borsuk number $b (n)$ of $n$ -dimensional Euclidean space $R^{n}$ is the smallest integer such that any set $F \subset R^{n}$ of unit diameter can be partitioned in…

math.MG2024

Optimal partitions of the flat torus into parts of smaller diameter

Dmitry Protasov, Alexander Tolmachev, Vsevolod Voronov

We consider the problem of partitioning a two-dimensional flat torus $T^{2}$ into $m$ sets in order to minimize the maximal diameter of a part. For $m ⩽ 25$ we give numerical…

A counterexample to Gale's conjecture in R3

Reducing the upper bound for the Borsuk number in R4 to 8

Optimal partitions of the flat torus into parts of smaller diameter

A counterexample to Gale's conjecture in $R^{3}$

Reducing the upper bound for the Borsuk number in $R^{4}$ to 8