English

On Blocking Numbers of Surfaces

Differential Geometry 2008-08-27 v3

Abstract

The blocking number of a manifold is the minimal number of points needed to block out lights between any two given points in the manifold. It has been conjectured that if the blocking number of a manifold is finite, then the manifold must be flat. In this paper we prove that this is true for 2-dimensional manifolds with non-trivial fundamental groups.

Keywords

Cite

@article{arxiv.0807.2934,
  title  = {On Blocking Numbers of Surfaces},
  author = {Wing Kai Ho},
  journal= {arXiv preprint arXiv:0807.2934},
  year   = {2008}
}

Comments

This is a very preliminary version of a paper about blocking numbers of compact Riemannian surfaces, the aim is to show that if the blocking number is finite, then the surface has to be flat. edit: similar results for 2-dimensional torus have been obtained by V. Bangert and E. Gutkin, reference to their paper has been added v3: minor changes with the references

R2 v1 2026-06-21T11:02:04.762Z