I. Nasonov

collaborators

3 papers

math.GT2026

Affine transverse foliations in sphere bundles

Ilya Alekseev, Ivan Nasonov, Gaiane Panina

Let~ $S^{n - 1} \to E \to M^{n}$ be an oriented sphere bundle supporting a smooth affine transverse foliation. We give an upper bound for the Euler number of the bundle.…

math.MG2026

On $2 n + 4$ normals conjecture for convex polytopes in $R^{n}$

Ivan Nasonov, Gaiane Panina

We prove that for $n > 3$ each generic simple polytope in $R^{n}$ contains a point with at least $2 n + 4$ emanating normals to the boundary. This result is a piecewise-linear co…

math.MG2025

Each generic polytope in $R^{3}$ has a point with ten normals to the boundary

Ivan Nasonov, Gaiane Panina

It is conjectured since long that each smooth convex body $P \subset R^{n}$ has a point in its interior which belongs to at least $2 n$ normals from different points…

Affine transverse foliations in sphere bundles

On 2n+4 normals conjecture for convex polytopes in Rn

Each generic polytope in R3 has a point with ten normals to the boundary

On $2 n + 4$ normals conjecture for convex polytopes in $R^{n}$

Each generic polytope in $R^{3}$ has a point with ten normals to the boundary