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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.00299 |
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Table of Contents:
- We prove that if $C$ is a symmetric convex body of revolution in $\mathbb R^4$ containing the unit Euclidean ball $\mathbb B_4$, such that the sections of $C$ by hyperplanes tangent to $\mathbb B_4$ have constant area $A>0$, then $C$ is a Euclidean ball, provided $\frac 1π \arctan((\frac{3A}{4π})^{1/3})$ satisfies certain arithmetic properties that can be read from its expansion as a continued fraction. We show that the set of values $A$ satisfying these properties has positive Hausdorff dimension.