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arXiv · 1201.0393

An asymmetric convex body with maximal sections of constant volume

Fedor Nazarov·Dmitry Ryabogin·Artem Zvavitch
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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.

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Fedor Nazarov, Dmitry Ryabogin, Artem Zvavitch. 2012-01-01. An asymmetric convex body with maximal sections of constant volume. https://arxiv.org/abs/1201.0393

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