English

3d steady Gradient Ricci Solitons with linear curvature decay

Differential Geometry 2016-12-20 v1

Abstract

In this note, we prove that a 3-dimensional steady Ricci soliton is rotationally symmetric if its scalar curvature R(x)R(x) satisfies C01ρ(x)R(x)C0ρ(x)\frac{C_0^{-1}}{\rho(x)}\le R(x)\le \frac{C_0}{\rho(x)} for some constant C0>0C_0>0, where ρ(x)\rho(x) denotes the distance from a fixed point x0x_0. Our result doesn't assume that the soliton is κ\kappa-noncollapsed.

Keywords

Cite

@article{arxiv.1612.05713,
  title  = {3d steady Gradient Ricci Solitons with linear curvature decay},
  author = {Yuxing Deng and Xiaohua Zhu},
  journal= {arXiv preprint arXiv:1612.05713},
  year   = {2016}
}