24 citations · 63 across the 13 of their papers we have counts for
16 papers
Geodesic nets on the Euclidean plane and closed geodesic nets on Euclidean surfaces
Ivan Frolov, Denis Gorodkov, Dmitrii Korshunov +1
We prove that if is a closed Riemannian surface of diameter and area with sectional curvature in the interval, then a closed geodesic net of length has at…
Small separators, upper bounds for -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 with its -width $W^{…
Boxing inequalities in Banach spaces and Riemannian manifolds
Sergey Avvakumov, Alexander Nabutovsky
We prove the following result: For each closed -dimensional manifold in a (finite or infinite-dimensional) Banach space , and each positive real there exists a…
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 that satisfy the following balancing condition: The sum of all unit tangent vectors to all ge…
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 -cycles (defined as finite collections of disjoint closed curves) parametrized by a sphere…
Linear bounds for constants in Gromov's systolic inequality and related results
Alexander Nabutovsky
Let be a closed Riemannian manifold. Larry Guth proved that there exists with the following property: if for some the volume of each metric ball of radius is…