11 citations · 11 across the 1 of their papers we have counts for
3 papers
math.DG2016★ 11 cited
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…
math.PR2016
Large deviations of convex hulls of planar random walks and Brownian motions
Arseniy Akopyan, Vladislav Vysotsky
We prove large deviations principles (LDPs) for the perimeter and the area of the convex hull of a planar random walk with finite Laplace transform of its increments. We give expli…
math.MG2015
Algebraic vertices of non-convex polyhedra
Arseniy Akopyan, Imre Bárány, Sinai Robins
In this article we define an algebraic vertex of a generalized polyhedron and show that it is the smallest set of points needed to define the polyhedron. We prove that the indicato…