2010/04/20 by Marlies Gerber, Gerber, Marlies, Wah-Kwan Ku +1
Mathematics · #53C22 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.DG #msc:53C22
paper · pdf · doi:10.48550/arxiv.1004.3593
arxiv created 2010/04/20 · openalex publication_date 2010/04/20 · arxiv updated 2010/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A pair of points (x,y) in a Riemannian manifold (M,g) is said to have the finite blocking property if there is a finite set P contained in M\x,y such that every geodesic segment from x to y passes through a point of P. We show that for every closed C-infinity manifold M of dimension at least two and every pair (x,y) in M x M, there exists a dense G-delta set of C-infinity Riemannian metrics on M such that (x,y) fails to have the finite blocking property for every g in that set.