Quasiconformal Rigidity of Negatively Curved Three Manifolds

2002/11/28 by Yong Hou, Hou, Yong
Mathematics · #57M50 #57M60 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Point processes and geometric inequalities #math.DG #math.GT #msc:57M50 #msc:57M60

paper · pdf · doi:10.48550/arxiv.math/0211440

arxiv created 2002/11/28 · openalex publication_date 2002/11/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the rigidity of infinite volume 3-manifolds with sectional curvature -b²≤ K≤ -1 and finitely generated fundamental group. In-particular, we generalize the Sullivan's quasi-conformal rigidity for finitely generated fundamental group with empty dissipative set to negative variable curvature 3-manifolds. We also generalize the rigidity of Hamenstädt or more recently Besson-Courtois-Gallot, to 3-manifolds with infinite volume and geometrically infinite fundamental group.

Related

• Quasi-isometric rigidity of three manifold groups
• On finite volume, negatively curved manifolds
• Large-scale conformal rigidity in dimension three
• Fundamental groups of finite volume, bounded negatively curved 4-manifolds are not 3-manifold groups
• On Mostow rigidity for variable negative curvature