2007/07/01 by Tobias Colding, Tobias H. Colding, Colding, Tobias H. +3 · 7 citations
Mathematics · Psychology · #Differential Geometry (math.DG) #Extinction (optical mineralogy) #FOS: Mathematics #Flow (mathematics) #Geology #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometry #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Mathematics #Mechanics #Paleontology #Physics #Psychology #Ricci curvature #Ricci flow #math.DG #math.GT
paper · pdf · doi:10.48550/arxiv.0707.0108
published in arXiv (Cornell University) (Cornell University)
arxiv created 2007/07/01 · openalex publication_date 2007/07/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
This is an expository article with complete proofs intended for a general non-specialist audience. The results are two-fold. First, we discuss a geometric invariant, that we call the width, of a manifold and show how it can be realized as the sum of areas of minimal 2-spheres. For instance, when M is a homotopy 3-sphere, the width is loosely speaking the area of the smallest 2-sphere needed to ``pull over'' M. Second, we use this to conclude that Hamilton's Ricci flow becomes extinct in finite time on any homotopy 3-sphere. We have chosen to write this since the results and ideas given here are quite useful and seem to be of interest to a wide audience.