83 citations · 542 across the 80 of their papers we have counts for
4 papers · 2 filters
Configuration-like spaces and coincidences of maps on orbits
R. N. Karasev, A. Yu. Volovikov
In this paper we study the spaces of -tuples of points in a Euclidean space, without -wise coincidences (configuration-like spaces). A transitive group action by permuting th…
Knaster's problem for almost -orbits
R. N. Karasev, A. Yu. Volovikov
In this paper some new cases of Knaster's problem on continuous maps from spheres are established. In particular, we consider an almost orbit of a -torus on the sphere, a co…
Periodic billiard trajectories in smooth convex bodies
R. N. Karasev
We consider billiard trajectories in a smooth convex body in and estimate the number of distinct periodic trajectories that make exactly reflections per period at…
Inscribing a regular crosspolytope
R. N. Karasev
In this paper we prove that it is possible to inscribe a regular crosspolytope (multidimensional octahedron) into a smooth convex body in , where is an odd prime p…