10 citations · 44 across the 9 of their papers we have counts for
9 papers
Dvoretzky type theorems for multivariate polynomials and sections of convex bodies
V. L. Dol'nikov, R. N. Karasev
In this paper we prove the Gromov--Milman conjecture (the Dvoretzky type theorem) for homogeneous polynomials on , and improve bounds on the number in the ana…
Tverberg-type theorems for intersecting by rays
R. N. Karasev
In this paper we consider some results on intersection between rays and a given family of convex, compact sets. These results are similar to the center point theorem, and Tverberg'…
The genus and the Lyusternik-Schnirelmann category of preimages
R. N. Karasev
In this paper some axiomatic generalization (function of open subsets) of the relative Lyusternik-Schnirelmann category is considered, incorporating the sectional category and the…
-index of the grassmanian
R. N. Karasev
We study the real Grassmann manifold (of -subspaces in ), and the action of on it by taking the orthogonal complement. The homological index of…
Regular embeddings of manifolds and topology of configuration spaces
R. N. Karasev
For a topological space we study continuous maps such that images of every pairwise distinct points are affinely (linearly) independent. Such maps ar…
Topological transversals to a family of convex sets
L. Montejano, R. N. Karasev
Let be a family of compact convex sets in . We say that has a \emph{topological -transversal of index } (, ) if…