English

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.

Keywords

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