A compactness theorem for gradient Ricci solitons is established via regularity bootstrapping in harmonic coordinates, implying smooth regular parts in noncollapsed limits with bounded Ricci curvature and asymptotic cylindricality for steady solitons with L1 Ricci decay.
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Steady soliton with $\mathcal{L}^{1}$ decay curvature
A compactness theorem for gradient Ricci solitons is established via regularity bootstrapping in harmonic coordinates, implying smooth regular parts in noncollapsed limits with bounded Ricci curvature and asymptotic cylindricality for steady solitons with L1 Ricci decay.