Gaiane Panina

activity

20202026

collaborators

10 papers

math.GT2026

Minimal quasisections of circle bundles

Ivan Kiselev, Gaiane Panina, Timur Shamazov

Let $E π B$ be an oriented circle bundle over an oriented closed surface, and let $E$ denote its Euler number. A \textit{quasisection} is a smooth surface $Q$ , p…

math.DG2026

Counting normals to closed curves in $R^{3}$

Gaiane Panina, Dirk Siersma

We prove the following results: (1) For every generic closed smooth curve in $R^{3}$ , {whose torsion has a constant sign}, there is a point with at least $6$ emanating norma…

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.CO2025

Lower bounds on the number of envy-free divisions

Duško Jojić, Gaiane Panina, Rade Živaljević

We analyze lower bounds for the number of envy-free divisions, in the classical Woodall-Stormquist setting and in a non-classical case, when envy-freeness is combined with the equi…

math.GT2024

A new proof of Milnor-Wood inequality

Gaiane Panina, Timur Shamazov, Maksim Turevskii

The Milnor-Wood inequality states that if a (topological) oriented circle bundle over an orientable surface of genus $g$ has a smooth transverse foliation, then the Euler class of…

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.GT2024

Quasisections of circle bundles and Euler class

Gaiane Panina, Timur Shamazov, Maksim Turevskii

Let $E π B$ be an oriented circle bundle over an oriented closed surface $B$ . A quasisection is a smooth surface $Q$ (either closed or bordered) mapped by a…

math.CO2024

Ky Fan theorem for sphere bundles

Gaiane Panina, Rade Živaljević

The classic Ky Fan theorem is a combinatorial equivalent of Borsuk-Ulam theorem. It is a generalization and extension of Tucker's lemma and, just like its predecessor, it pinpoints…

math.AT2023

Minimal triangulations of circle bundles

Gaiane Panina, Maksim Turevskii

A triangulation of a circle bundle $E π B$ is a triangulation of the total space $E$ and the base $B$ such that the projection $π$ is a simplicial map. In the…

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…