Some type i solutions of ricci flow with rotational symmetry

TY - JOUR

T1 - Some type i solutions of ricci flow with rotational symmetry

AU - Song, Jian

N1 - Funding Information: This research was supported in part by National Science Foundation grant DMS-0847524 and a Sloan Foundation Fellowship. The author thank Zhenlei Zhang for many stimulating discussions. He also thank Huai-Dong Cao and Valentino Tosatti for many helpful suggestions. Publisher Copyright: © 2014 The Author(s).

PY - 2015

Y1 - 2015

N2 - 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 nonflat shrinking gradient Kahler-Ricci soliton on a complete Kahler manifold homeomorphic to Cn blown-up at one point.

AB - 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 nonflat shrinking gradient Kahler-Ricci soliton on a complete Kahler manifold homeomorphic to Cn blown-up at one point.

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U2 - https://doi.org/10.1093/imrn/rnu134

DO - https://doi.org/10.1093/imrn/rnu134

M3 - Article

SN - 1073-7928

VL - 2015

SP - 7365

EP - 7381

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 16

ER -