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arXiv · 2606.21112

Illumination bodies on Riemannian manifolds

Rotem Assouline·Carsten Schütt·Elisabeth M. Werner
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Abstract

We prove a generalization of Werner's asymptotic formula for the volume of the illumination body of a convex body, which holds on Riemannian manifolds with Ricci curvature bounded from below. The $\delta$-illumination body of a subset of a Riemannian manifold is defined to be the set of all points such that the union of all minimizing geodesic segments joining the point to the set has volume at most $\delta$.

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Rotem Assouline, Carsten Schütt, Elisabeth M. Werner. 2026-06-19. Illumination bodies on Riemannian manifolds. https://arxiv.org/abs/2606.21112

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