A. Nabutovsky

activity

19922026

most citedNoncomputability Arising In Dynamical Triangulation Model Of Four-Dimensional Quantum Gravity

24 citations · 63 across the 13 of their papers we have counts for

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9 papers · 1 filter

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.DG2024

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.DG2022

Geodesic nets on non-compact Riemannian manifolds

Gregory R. Chambers, Yevgeny Liokumovich, Alexander Nabutovsky +1

A geodesic flower is a finite collection of geodesic loops based at the same point $p$ that satisfy the following balancing condition: The sum of all unit tangent vectors to all ge…

math.DG2020

Sweepouts of closed Riemannian manifolds

Alexander Nabutovsky, Regina Rotman, Stéphane Sabourau

We show that for every closed Riemannian manifold there exists a continuous family of $1$ -cycles (defined as finite collections of disjoint closed curves) parametrized by a sphere…

math.DG2019

Filling metric spaces

Yevgeny Liokumovich, Boris Lishak, Alexander Nabutovsky +1

We prove a new version of isoperimetric inequality: Given a positive real $m$ , a Banach space $B$ , a closed subset $Y$ of metric space $X$ and a continuous map $f : Y \to B$ …

math.DG2014

Lengths of three simple periodic geodesics on a Riemannian $2$ -sphere

Yevgeny Liokumovich, Alexander Nabutovsky, Regina Rotman

Let $M$ be a Riemannian $2$ -sphere. A classical theorem of Lyusternik and Shnirelman asserts the existence of three distinct simple non-trivial periodic geodesics on $M$ . In this p…