83 citations · 542 across the 80 of their papers we have counts for
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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…
Orthogonal shadows and index of Grassmann manifolds
Djordje Baralić, Pavle V. M. Blagojević, Roman Karasev +1
In this paper we study the action on real Grassmann manifolds and given by taking (appropriately oriented) orthogonal complemen…
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…
Optimality of codes with respect to error probability in Gaussian noise
Alexey Balitskiy, Roman Karasev, Alexander Tsigler
We consider geometrical optimization problems related to optimizing the error probability in the presence of a Gaussian noise. One famous questions in the field is the "weak simple…