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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.29130 |
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Table of Contents:
- In his classical work, W. Blaschke proved that a convex body whose shadow boundaries are flat for every direction of parallel illumination must be an ellipsoid. An extension recently proposed by I. Gonzalez-García, J. Jerónimo-Castro, E. Morales-Amaya, and D.J. Verdusco-Hernández predicts that the same conclusion holds for illumination by point light sources located on a hypersurface enclosing the body. We confirm this conjecture for convex bodies with sufficiently smooth boundaries. We further develop a duality framework relating illumination by point light sources to classical symmetry properties of hyperplane sections, linking several known and conjectured characterizations of quadrics from these complementary viewpoints.