An asymmetric convex body with maximal sections of constant volume
Metric Geometry
2012-01-04 v1
Abstract
We show that in all dimensions d>2, there exists an asymmetric convex body of revolution all of whose maximal hyperplane sections have the same volume. This gives the negative answer to the question posed by V. Klee in 1969.
Cite
@article{arxiv.1201.0393,
title = {An asymmetric convex body with maximal sections of constant volume},
author = {Fedor Nazarov and Dmitry Ryabogin and Artem Zvavitch},
journal= {arXiv preprint arXiv:1201.0393},
year = {2012}
}
Comments
29 pages, 5 figures