English

Some Type I solutions of Ricci flow with rotational symmetry

Differential Geometry 2012-03-14 v1 Analysis of PDEs

Abstract

We prove that the Ricci flow on CP^n 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 C^n blown-up at one point.

Keywords

Cite

@article{arxiv.1203.2688,
  title  = {Some Type I solutions of Ricci flow with rotational symmetry},
  author = {Jian Song},
  journal= {arXiv preprint arXiv:1203.2688},
  year   = {2012}
}