Blocking Light in Compact Riemannian Manifolds

  title={Blocking Light in Compact Riemannian Manifolds},
  author={J. Lafont and Benjamin Schmidt},
We study compact Riemannian manifolds .M; g/ for which the light from any given point x 2 M can be shaded away from any other point y 2 M by finitely many point shades in M . Compact flat Riemannian manifolds are known to have this finite blocking property. We conjecture that amongst compact Riemannian manifolds this finite blocking property characterizes the flat metrics. Using entropy considerations, we verify this conjecture amongst metrics with nonpositive sectional curvatures. Using the… CONTINUE READING

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