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arXiv · 2605.25122

Illumination Bodies in Projective Geometries

Rotem Assouline·Florian Besau·Elisabeth M. Werner
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Abstract

We extend the notion of illumination bodies to Riemannian spaces of constant curvature and to projective Finsler geometries. We prove that the derivative of their volume defines a notion of surface area for convex bodies in these settings, generalizing the affine surface area in Euclidean space. The proof is based on a general result on the derivative of weighted volumes of weighted illumination bodies in Euclidean space. In the appendix, we give some explicit examples for non-Euclidean illumination bodies.

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Rotem Assouline, Florian Besau, Elisabeth M. Werner. 2026-05-24. Illumination Bodies in Projective Geometries. https://arxiv.org/abs/2605.25122

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