On manifolds with quadratic curvature decay

2005/10/27 by Nader Yeganefar · 4 citations
Mathematics · #Combinatorics #Curvature #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry #Geometry and complex manifolds #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Pure mathematics #Quadratic equation #Scalar curvature #Sectional curvature #Topology (electrical circuits) #Type (biology) #math.DG

paper · pdf · doi:10.1112/s0010437x09003947

published in Compositio Mathematica 145(2), 528-540 (Cambridge University Press)

arxiv created 2005/10/27 · openalex publication_date 2009/03/01 · arxiv updated 2014/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Abstract We give conditions which imply that a complete noncompact manifold with quadratic curvature decay has finite topological type. In particular, we find links between the topology of a manifold with quadratic curvature decay and some properties of the asymptotic cones of such a manifold.

Citations

• Metric Structures for Riemannian and Non-Riemannian Spaces
• Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds
• Hyperbolic Manifolds and Discrete Groups
• On the Structure of Complete Manifolds of Nonnegative Curvature
• Ricci curvature and the topology of open manifolds