2012/02/29 by S. Brendle, Simon Brendle · 3 citations
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #math.AP #math.DG
paper · pdf · doi:10.1007/s00222-013-0457-0
Final version, to appear in Invent. Math
arxiv created 2013/02/03 · openalex publication_date 2013/02/12 · crossref created 2013/02/12 · crossref issued 2013/02/13 · crossref published 2013/02/13 · crossref published-online 2013/02/13 · crossref published-print 2013/12/01 · arxiv updated 2015/06/04 · openalex created_date 2016/06/24 · crossref deposited 2019/05/24 · crossref indexed 2026/07/13 · openalex updated_date 2026/07/29
Let (M,g) be a three-dimensional steady gradient Ricci soliton which is non-flat and κ-noncollapsed. We prove that (M,g) is isometric to the Bryant soliton up to scaling. This solves a problem mentioned in Perelman's first paper.