2018/12/10 by Xiaolong Li, Yongjia Zhang, Li, Xiaolong +1
Mathematics · Physics and Astronomy · #53C44 #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AP #math.DG #msc:53C44
paper · pdf · doi:10.48550/arxiv.1812.04156
Final version, to appear in Communications in Analysis and Geometry
openalex publication_date 2018/12/10 · arxiv created 2020/05/14 · arxiv updated 2020/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study κ-noncollapsed ancient solutions to the Ricci flow with nonnegative curvature operator in higher dimensions. We impose one further assumption: one of the asymptotic shrinking gradient Ricci solitons is the standard cylinder \mathbbSn-1×ℝ. By making use of the properties of such ancient solutions, we generalize part one of Brendle \citebrendle2018ancient to higher dimensions, that is, every noncompact κ-noncollapsed rotationally symmetric ancient solution to the Ricci flow with bounded positive curvature operator must be the Bryant soliton.