2002/10/28 by Sylvain Maillot, Maillot, Sylvain
Mathematics · #20F69 #53A30 (Primary) 20F65 #57M50 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #math.DG #math.GR #math.GT #msc:20F65 #msc:20F69 #msc:53A30 #msc:57M50
paper · pdf · doi:10.48550/arxiv.math/0210433
22 pages, 2 figures
arxiv created 2002/10/28 · openalex publication_date 2002/10/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define a complete Riemannian manifold X to be large-scale conformally rigid if all groups that are quasi-isometric to some complete Riemannian manifold of bounded geometry conformal to X are quasi-isometric to X. We prove that many 3-manifolds, including Euclidean 3-space, hyperbolic 3-space and the product of the hyperbolic plane with the real line are large-scale conformally rigid. This implies new characterizations of groups that can act properly, cocompactly by isometries on those manifolds.