On Potential Function of Gradient Steady Ricci Solitons

Details On Potential Function of Gradient Steady Ricci Solitons On Potential Function of Gradient Steady Ricci Solitons

2011-02-15

arxiv.org/abs/1102.3018v2

Mathematics

Differential Geometry

7 pages, proof of the main theorem revised

Scientific paper

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.

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