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- W2971060766 abstract "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 $overline{lim}_{rto infty} r|Rm|<frac{1}{5}$, 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 $Sto 0$ as $rto infty$, 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 $overline{lim}_{rto infty} rS$ is sufficiently small and $f$ is bounded above by a constant." @default.
- W2971060766 created "2019-09-05" @default.
- W2971060766 creator A5051552943 @default.
- W2971060766 date "2019-08-27" @default.
- W2971060766 modified "2023-10-14" @default.
- W2971060766 title "Curvature estimates for steady Ricci solitons" @default.
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- W2971060766 doi "https://doi.org/10.48550/arxiv.1908.10456" @default.
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