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Curvature estimates for steady Ricci solitons by Chan, Pak-Yeung is a scholarly article available to read on EtoBox.

What is Curvature estimates for steady Ricci solitons about?

We show that for an $n$ dimensional complete non Ricci flat gradient steady Ricci soliton with potential function $f$ bounded above by a constant and curvature tensor $Rm$ satisfying $\overline{\lim}_{r\to \infty} r|Rm|<\frac{1}{5}$, then $|Rm|\leq Ce^{-r}$ for some constant $C>0$, improving a result of [36]. For any four dimensional complete non Ricci flat gradient steady Ricci soliton with scalar curvature $S\to 0$ as $r\to \infty$, we prove that $|Rm|\leq cS$ for some constant $c>0$, improving an estimate in [11]. As an application, we show that for a four dimensional complete non Ricci flat gradient steady Ricci soliton, $|Rm|$ decays exponentially provided that $\overline{\lim}_{r\to \infty} rS$ is sufficiently small and $f$ is bounded above by a constant.

Author

Chan, Pak-Yeung

Published

2019

Language

EN