3d steady Gradient Ricci Solitons with linear curvature decay

2016/12/17 by Deng, Yuxing, Zhu, Xiaohua
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1612.05713

Abstract

In this note, we prove that a 3-dimensional steady Ricci soliton is rotationally symmetric if its scalar curvature R(x) satisfies \fracC₀^-1ρ(x)≤ R(x)≤ (C₀)/(ρ(x)) for some constant C₀>0, where ρ(x) denotes the distance from a fixed point x₀. Our result doesn't assume that the soliton is κ-noncollapsed.

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