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.
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