New Proofs of Perelman’s Theorem on Shrinking Breathers in Ricci Flow
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We give two new proofs of Perelman’s theorem that shrinking breathers of Ricci flow on closed manifolds are gradient Ricci solitons, using the fact that the singularity models of Type I solutions are shrinking gradient Ricci solitons and the fact that non-collapsed Type I ancient solutions have rescaled limits being shrinking gradient Ricci solitons.
KeywordsRicci flow Shrinking breathers Type I solutions Gradient Ricci solitons
Mathematics Subject Classification53C44
P. L. wants to thank Professor Li, Jiayu and School of Mathematical Sciences at the University of Science and Technology of China, where part of this work is carried out, for their warm hospitality during spring, 2017. The authors thank the referee for detailed suggestions which helped to improve the paper.