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, Vladyslav, Yaskin
TL;DR
This paper proves that the fifth and eighth Busemann-Petty problems have positive solutions for bodies close to the Euclidean ball, advancing understanding of convex geometric inequalities near the Euclidean setting.
Contribution
It establishes positive solutions to the fifth and eighth Busemann-Petty problems for bodies near the Euclidean ball in Banach-Mazur distance.
Findings
Positive solutions for bodies close to Euclidean ball
Extension of Busemann-Petty problem results
Advances in convex geometric inequalities
Abstract
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.
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