24 citations · 143 across the 29 of their papers we have counts for
4 papers · 2 filters
Estimating symplectic capacities from lengths of closed curves on the unit spheres
Arseniy Akopyan, Roman Karasev
We improve the estimates for the Ekeland--Hofer--Zehnder capacity of convex bodies by Gluskin and Ostrover. In the course of our argument we show that a closed characteristic of mi…
Any cyclic quadrilateral can be inscribed in any closed convex smooth curve
Arseniy Akopyan, Sergey Avvakumov
We prove that any cyclic quadrilateral can be inscribed in any closed convex -curve. The smoothness condition is not required if the quadrilateral is a rectangle.
Two circles and only a straightedge
Arseniy Akopyan, Roman Fedorov
We answer a question of David Hilbert: given two circles it is not possible in general to construct their centers using only a straightedge. On the other hand, we give infinitely m…
Waist of balls in hyperbolic and spherical spaces
Arseniy Akopyan, Roman Karasev
In this paper we find a tight estimate for Gromov's waist of the balls in spaces of constant curvature, deduce the estimates for the balls in Riemannian manifolds with upper bounds…