83 citations · 542 across the 80 of their papers we have counts for
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Lower and upper bounds for the waists of different spaces
Arseniy Akopyan, Alfredo Hubard, Roman Karasev
We prove several new results around Gromov's waist theorem. We give a simple proof of Vaaler's theorem on sections of the unit cube using the Borsuk--Ulam--Crofton technique. We co…
A tight estimate for the waist of the ball
Arseniy Akopyan, Roman Karasev
We answer a question of M. Gromov on the waist of the unit ball.
A center transversal theorem for an improved Rado depth
Pavle V. M. Blagojević, Roman Karasev, Alexander Magazinov
A celebrated result of Dol'nikov, and of Živaljević and Vrećica, asserts that for every collection of measures on the Euclidean space th…
Local multiplicity of continuous maps between manifolds
Pavle V. M. Blagojević, Roman Karasev
Let and be smooth (real or complex) manifolds, and let be equipped with some Riemannian metric. A continuous map admits a local -multipl…
Dependence of the heavily covered point on parameters
Alexey Balitskiy, Roman Karasev
We examine Gromov's method of selecting a point "heavily covered" by simplices formed by a given finite point sets, in order to understand the dependence of the heavily covered poi…