Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Physical Sciences and Mathematics
On The Busemann-Petty Problem Concerning Central Sections Of Centrally Symmetric Convex-Bodies, Richard J. Gardner
On The Busemann-Petty Problem Concerning Central Sections Of Centrally Symmetric Convex-Bodies, Richard J. Gardner
Mathematics Faculty Publications
We present a method which shows that in E3 the Busemann-Petty problem, concerning central sections of centrally symmetric convex bodies, has a positive answer. Together with other results, this settles the problem in each dimension.
Intersection Bodies And The Busemann-Petty Problem, Richard J. Gardner
Intersection Bodies And The Busemann-Petty Problem, Richard J. Gardner
Mathematics Faculty Publications
It is proved that the answer to the Busemann-Petty problem concerning central sections of centrally symmetric convex bodies in d-dimensional Euclidean space Ed is negative for a given d if and only if certain centrally symmetric convex bodies exist in Ed which are not intersection bodies. It is also shown that a cylinder in Ed is an intersection body if and only if d ≤ 4, and that suitably smooth axis-convex bodies of revolution are intersection bodies when d ≤ 4. These results show that the Busemann-Petty problem has a negative answer for d ≥ 5 …