2012/09/25 by Davi Máximo · 1 citation
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Advanced Differential Geometry Research #Gravitational singularity #Ricci flow #Mathematics #Singularity #Limit (mathematics) #Manifold (fluid mechanics) #Flow (mathematics) #Curvature #Conjecture #Pure mathematics #Mathematical analysis #Metric (unit) #Type (biology) #Mathematical physics #Ricci curvature #Geometry #Geology
paper · doi:10.1515/crelle-2012-0080
openalex publication_date 2012/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Abstract. In this paper we prove a conjecture by Feldman–Ilmanen–Knopf (2003) that the gradient shrinking soliton metric they constructed on the tautological line bundle over <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi>ℂℙ</m:mi> <m:mn>1</m:mn> </m:msup> </m:math> \mathbb CP1 is the uniform limit of blow-ups of a type I Ricci flow singularity on a closed manifold. We use this result to show that limits of blow-ups of Ricci flow singularities on closed four-dimensional manifolds do not necessarily have non-negative Ricci curvature.