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We study  blow-ups around fixed points  at Type I singularities of the Ricci flow on closed manifolds using Perelman's -functional. First, we give an alternative proof of the result obtained by Naber (2010) and Enders–Müller–Topping (2011) that blow-up limits are non-flat gradient shrinking Ricci solitons. Our second and main result relates a  limit -density  at a Type I singular point to the  entropy  of the limit gradient shrinking soliton obtained by blowing-up at this point. In particular, we show that no entropy is lost at infinity during the blow-up process.

Perelman's entropy functional at Type I singularities of the Ricci flow