Addendum to “Perelman’s reduced volume and a gap theorem for the Ricci flow”

In this addendum [to the current author’s original paper published in CAG vol. 17, no. 2, 2009], we prove that if the Gaussian density of a complete gradient shrinking Ricci soliton is close to that of the Gaussian soliton, then they are isometric to each other. This was shown in [the original paper] under the additional assumption that its Ricci curvature is bounded below. We drop this assumption by developing Perelman’s reduced geometry for arbitrary complete gradient shrinking Ricci solitons.

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Published 9 April 2013