83 citations · 542 across the 80 of their papers we have counts for
9 papers · 1 filter
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…
Dual central point theorems and their generalizations
R. N. Karasev
We prove some analogues of the central point theorem and Tverberg's theorem, where instead of points, we consider hyperplanes or affine flats of given dimension.
KKM-type theorems for products of simplices and cutting sets and measures by straight lines
R. N. Karasev
In this paper a version of Knaster-Kuratowski-Mazurkiewicz theorem for products of simplices is formulated. Some corollaries for measure partition in the plane and cutting families…
Knaster's problem for -symmetric subsets of the sphere
R. N. Karasev
We prove a Knaster-type result for orbits of the group in , calculating the Euler class obstruction. Among the consequences are: a result about inscribing skew…
Analogues of the central point theorem for families with -intersection property in
R. N. Karasev
In this paper we consider families of compact convex sets in such that any subfamily of size at most has a nonempty intersection. We prove some analogues of the c…
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…