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arXiv · 2304.07074

On star-convex bodies with rotationally invariant sections

Bartłomiej Zawalski
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Abstract

We will prove that an origin-symmetric star-convex body $K$ with sufficiently smooth boundary and such that every hyperplane section of $K$ passing through the origin is a body of affine revolution, is itself a body of affine revolution. This will give a positive answer to the recent question asked by G. Bor, L. Hern\'andez-Lamoneda, V. Jim\'enez de Santiago, and L. Montejano-Peimbert, though with slightly different prerequisites.

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Bartłomiej Zawalski. 2023-04-14. On star-convex bodies with rotationally invariant sections. https://doi.org/10.1007/s13366-023-00702-1

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