D. Ryabogin

activity

20172021

collaborators

3 papers

math.MG2021

A solution to the Fifth and the Eighth Busemann-Petty problems in a small neighborhood of the Euclidean ball

M. Angeles Alfonseca, Fedor Nazarov, Dmitry Ryabogin +1

We show that the fifth and the eighth Busemann-Petty problems have positive solutions for bodies that are sufficiently close to the Euclidean ball in the Banach-Mazur distance.

math.MG2018

On bodies in $R^{5}$ with directly congruent projections or sections

M. Angeles Alfonseca, Michelle Cordier, Dmitry Ryabogin

Let $K$ and $L$ be two convex bodies in $R^{5}$ with countably many diameters, such that their projections onto all $4$ dimensional subspaces containing one fixed diameter…

math.CA2017

Fine approximation of convex bodies by polytopes

Márton Naszódi, Fedor Nazarov, Dmitry Ryabogin

We prove that for every convex body $K$ with the center of mass at the origin and every $ε \in (0, \frac{1}{2})$ , there exists a convex polytope $P$ with at most…

A solution to the Fifth and the Eighth Busemann-Petty problems in a small neighborhood of the Euclidean ball

On bodies in R5 with directly congruent projections or sections

Fine approximation of convex bodies by polytopes

On bodies in $R^{5}$ with directly congruent projections or sections