7 citations · 7 across the 1 of their papers we have counts for
3 papers
math.MG2026★ 7 cited
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…
math.MG2025
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…
math.AT2024
Topological lower bounds on the sizes of simplicial complexes and simplicial sets
Sergey Avvakumov, Roman Karasev
We prove that if an -dimensional space satisfies certain topological conditions then any triangulation of as well as any its representation as a simplicial set with cont…