D. Ryabogin

activity

20172022

most citedAn analog of polynomially integrable bodies in even-dimensional spaces

1 citations · 1 across the 3 of their papers we have counts for

collaborators

Showing math.MGShow all

4 papers · 1 filter

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.MG2020

On an equichordal property of a pair of convex bodies

Dmitry Ryabogin

Let $d \geq 2$ and let $K$ and $L$ be two convex bodies in $R^{d}$ such that $L \subset int K$ and the boundary of $L$ does not contain a segment. If $K$ and $L$ sat…

math.MG2020

On bodies floating in equilibrium in every orientation

Dmitry Ryabogin

Ulam's problem 19 from the Scottish Book asks: {\it is a solid of uniform density which floats in water in every position necessarily a sphere?} We obtain several results related t…

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…

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

On an equichordal property of a pair of convex bodies

On bodies floating in equilibrium in every orientation

On bodies in R5 with directly congruent projections or sections

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