English

A no expanding breather theorem for noncompact Ricci flows

Differential Geometry 2021-04-08 v1

Abstract

In this note we show that, under certain curvature positivity conditions (the weak PIC2\operatorname{PIC}-2 condition or the nonnegative bisectional curvature condition), a complete and noncompact expanding breather of the Ricci flow is also an expanding gradient Ricci soliton. This is the first no expanding breather theorem in the noncompact category.

Keywords

Cite

@article{arxiv.2104.02834,
  title  = {A no expanding breather theorem for noncompact Ricci flows},
  author = {Liang Cheng and Yongjia Zhang},
  journal= {arXiv preprint arXiv:2104.02834},
  year   = {2021}
}

Comments

11 pages

R2 v1 2026-06-24T00:54:26.298Z