English

On Potential Function of Gradient Steady Ricci Solitons

Differential Geometry 2014-11-18 v2

Abstract

In this paper we study potential function of gradient steady Ricci solitons. We prove that infimum of potential function decays linearly; in particular, potential function of rectifiable gradient steady Ricci solitons decays linearly. As a consequence, we show that a gradient steady Ricci soliton with bounded potential function must be trivial, and no gradient steady Ricci soliton admits uniformly positive scalar curvature.

Keywords

Cite

@article{arxiv.1102.3018,
  title  = {On Potential Function of Gradient Steady Ricci Solitons},
  author = {Peng Wu},
  journal= {arXiv preprint arXiv:1102.3018},
  year   = {2014}
}

Comments

7 pages, proof of the main theorem revised

R2 v1 2026-06-21T17:26:25.426Z