Three-dimensional Steady Gradient Ricci Solitons with Linear Curvature Decay. (14th July 2017)

• Record Type: Journal Article
• Authors: Deng, Yuxing; Zhu, Xiaohua
• Is Part Of: International mathematics research notices. Volume 2019:Number 4(2019)
• Page Start: 1108
• Page End: 1124
• Publication Date: 2017-07-14
• Subjects: Primary: 53C25 -- Secondary: 53C55 -- 58J05; Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnx155
• Languages: English
• ISSNs: 1073-7928

Abstract

Abstract: In this note, we prove that a three-dimensional steady Ricci soliton is rotationally symmetric if its scalar curvature R ( x ) satisfies C 0 − 1 ρ ( x ) ≤ R ( x ) ≤ C 0 ρ ( x ) for some constant C 0 > 0, where ρ ( x ) denotes the distance from a fixed point x 0 . Our result does not assume that the soliton is κ -noncollapsed.