Some Type I solutions of Ricci flow with rotational symmetry

2012/03/13 by Jian Song, Song, Jian
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #math.AP #math.DG

paper · pdf · doi:10.48550/arxiv.1203.2688

arxiv created 2012/03/13 · arxiv updated 2012/03/14

Abstract

We prove that the Ricci flow on CPⁿ blown-up at one point starting with any rotationally symmetric Kahler metric must develop Type I singularities. In particular, if the total volume does not go to zero at the singular time, the parabolic blow-up limit of the Type I Ricci flow along the exceptional divisor is a complete non-flat shrinking gradient Kahler-Ricci soliton on a complete Kahler manifold homeomorphic to Cⁿ blown-up at one point.

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