2006/07/31 by Jean-François Lafont, J. -F. Lafont, B. Schmidt +1
Materials Science · Mathematics · #Blocking (statistics) #Conjecture #Euclidean geometry #Geometric Analysis and Curvature Flows #Morphological variations and asymmetry #Point (geometry) #Quasicrystal Structures and Properties #Quotient #Riemannian geometry #Riemannian manifold #math.DG #math.GT
paper · pdf · doi:10.2140/gt.2007.11.867
published as Geom. Topol. 11 (2007) 867-887 · 19 pages
arxiv created 2006/07/31 · openalex publication_date 2007/05/27 · arxiv updated 2014/11/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 same approach, K Burns and E Gutkin have independently obtained this result. Additionally, we show that compact quotients of Euclidean buildings have the finite blocking property.