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arXiv · 0704.3642

A characterization of round spheres in terms of blocking light

Benjamin Schmidt·Juan Souto
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Abstract

A closed Riemannian manifold is said to have cross blocking if whenever distinct points p and q are at distance less than the diameter, all light rays from p can be shaded away from q with at most two point shades. Similarly, a closed Riemannian manifold is said to have sphere blocking if for each point p, all the light rays from p are shaded away from p by a single point shade. We prove that Riemannian manifolds with cross and sphere blocking are isometric to round spheres.

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Benjamin Schmidt, Juan Souto. 2008-03-14. A characterization of round spheres in terms of blocking light. https://arxiv.org/abs/0704.3642

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