Gaiane Panina

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20202026

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math.MG2025

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.MG2024

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…

math.MG2020

Colored Tverberg problem, extensions and new results

Duško Jojić, Gaiane Panina, Rade T. Živaljević

We prove a "multiple colored Tverberg theorem" and a "balanced colored Tverberg theorem", by applying different methods, tools and ideas. The proof of the first theorem uses multip…

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

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

Colored Tverberg problem, extensions and new results

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