Gaiane Panina

activity

20242026

collaborators

8 papers

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 $R^{3}$ there is a point with at least $6$ emanating normals to the curve. (2) For every generic…

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.GT2025

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.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…

math.CO2025

Lower bounds on the number of envy-free divisions

DuÅ¡ko JojiÄ, Gaiane Panina, Rade Å½ivaljeviÄ

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.GT2025

Quasisections of circle bundles and Euler class

Gaiane Panina, Timur Shamazov, Maksim Turevskii

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