3 papers
math.FA2026
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…
math.FA2026
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…
math.FA2023
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|…