3 citations · 3 across the 5 of their papers we have counts for
6 papers
Zong's problem on half-spaces containing the unit ball
Grigory Ivanov
We prove that the intersection of halfspaces containing the Euclidean unit ball in contains a point of norm at least . Equality characterizes the cube…
A colorful quantitative Helly theorem for volume
Grigory Ivanov
We prove a colorful quantitative Helly theorem for volume with the optimal number of colors. If every rainbow intersection from finite families of convex sets in h…
A colorful Steinitz theorem with different centers
G. Ivanov
We prove a colorful quantitative Steinitz theorem in which the color classes may have different centers. If the convex hull of each of sets in contains a translate of t…
The maximal volume of projections of the cross-polytope
Grigory Ivanov
We prove the conjectured sharp upper bound for the volume of an arbitrary lower-dimensional orthogonal projection of the regular cross-polytope. More generally, for every spanning…
Optimality of no-dimensional bounds in Banach spaces
Grigory Ivanov, Vladimir Kadets
We discuss lower-bound constructions for several no-dimensional theorems of combinatorial geometry in Banach spaces. The common mechanism is the Maurey--Pisier theorem: the suprema…
Shortest curves in proximally smooth sets: existence and uniqueness
Grigory M. Ivanov, Mariana S. Lopushanski, Grigorii E. Ivanov
We study shortest curves in proximally smooth subsets of a Hilbert space. We consider an -proximally smooth set in a Hilbert space with points and satisfying $\left|…