English

A note on Perelman's no shrinking breather theorem

Differential Geometry 2018-04-27 v2

Abstract

As an application of his entropy formula, Perelman proved that every compact shrinking breather is a shrinking gradient Ricci soliton. We give a proof for the complete noncompact case by using Perelman's L\mathcal{L}-geometry. Our proof follows the argument in Lu and Zheng of constructing an ancient solution, and removes a technical assumption made by them.

Cite

@article{arxiv.1803.03660,
  title  = {A note on Perelman's no shrinking breather theorem},
  author = {Yongjia Zhang},
  journal= {arXiv preprint arXiv:1803.03660},
  year   = {2018}
}
R2 v1 2026-06-23T00:48:05.432Z