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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | https://arxiv.org/abs/2603.29130 |
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| _version_ | 1866911556349984768 |
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| author | Zawalski, Bartłomiej |
| author_facet | Zawalski, Bartłomiej |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29130 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On flat shadow boundaries from point light sources and the characterization of ellipsoids Zawalski, Bartłomiej Metric Geometry Primary 53A07, Secondary 05D10, 15A69, 52A20, 53A15 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. |
| title | On flat shadow boundaries from point light sources and the characterization of ellipsoids |
| topic | Metric Geometry Primary 53A07, Secondary 05D10, 15A69, 52A20, 53A15 |
| url | https://arxiv.org/abs/2603.29130 |