A. Nabutovsky

collaborators

3 papers

math.DG2026

Geodesic nets on the Euclidean plane and closed geodesic nets on Euclidean surfaces

Ivan Frolov, Denis Gorodkov, Dmitrii Korshunov +1

We prove that if $M$ is a closed Riemannian surface of diameter $d$ and area $v$ with sectional curvature in the $[- 1, 1]$ interval, then a closed geodesic net of length $l$ has at…

math.DG2025

Small separators, upper bounds for $l^{\infty}$ -widths, and systolic geometry

Sergey Avvakumov, Alexander Nabutovsky

We investigate the dependence on the dimension in the inequalities that relate the Euclidean volume of a closed submanifold $M^{n} \subset R^{N}$ with its $l^{\infty}$ -width $W^{…

math.MG2025

Boxing inequalities in Banach spaces and Riemannian manifolds

Sergey Avvakumov, Alexander Nabutovsky

We prove the following result: For each closed $n$ -dimensional manifold $M$ in a (finite or infinite-dimensional) Banach space $B$ , and each positive real $m \leq n$ there exists a…

Geodesic nets on the Euclidean plane and closed geodesic nets on Euclidean surfaces

Small separators, upper bounds for l∞-widths, and systolic geometry

Boxing inequalities in Banach spaces and Riemannian manifolds

Small separators, upper bounds for $l^{\infty}$ -widths, and systolic geometry