Rotational symmetry of self-similar solutions to the Ricci flow

• 成果类型: Article
• 署名作者: Brendle, Simon
• 署名单位: Stanford University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-013-0457-0
• 发表日期: 2013
• 页码: 731-764
• 关键词: curvature; solitons; 3-manifolds; uniqueness

摘要

Let (M,g) be a three-dimensional steady gradient Ricci soliton which is non-flat and kappa-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.