18 citations · 63 across the 14 of their papers we have counts for
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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…
Systolic inequalities for the number of vertices
Sergey Avvakumov, Alexey Balitskiy, Alfredo Hubard +1
Inspired by the classical Riemannian systolic inequality of Gromov we present a combinatorial analogue providing a lower bound on the number of vertices of a simplicial complex in…
Equipartition of a segment
Sergey Avvakumov, Roman Karasev
We prove that, for any positive integer , a segment may be partitioned into possibly degenerate or empty segments with equal values of a continuous function of a segment…
Convex fair partitions into an arbitrary number of pieces
Arseniy Akopyan, Sergey Avvakumov, Roman Karasev
We prove that any convex body in the plane can be partitioned into convex parts of equal areas and perimeters for any integer ; this result was previously known for pri…
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.