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5 papers · 2 filters
Flexible cross-polytopes in spaces of constant curvature
Alexander A. Gaifullin
We construct self-intersected flexible cross-polytopes in the spaces of constant curvature, that is, the Euclidean spaces, the spheres, and the Lobachevsky spaces of all dimensions…
Topology of geometric joins
Imre Barany, Andreas F. Holmsen, Roman Karasev
We consider the geometric join of a family of subsets of the Euclidean space. This is a construction frequently used in the (colorful) Carathéodory and Tverberg theorems, and their…
Another ham sandwich in the plane
Alexey Balitskiy, Alexey Garber, Roman Karasev
We show that every two nice measures in the plane can be partitioned into equal halves by translation of an angle from arbitrary k-fan when k is odd and in some cases when k is eve…
Deformations of period lattices of flexible polyhedral surfaces
Alexander A. Gaifullin, Sergey A. Gaifullin
In the end of the 19th century Bricard discovered a phenomenon of flexible polyhedra, that is, polyhedra with rigid faces and hinges at edges that admit non-trivial flexes. One of…
Convex Equipartitions: The Spicy Chicken Theorem
Roman Karasev, Alfredo Hubard, Boris Aronov
We show that, for any prime power n and any convex body K (i.e., a compact convex set with interior) in Rd, there exists a partition of K into n convex sets with equal volumes and…