A no expanding breather theorem for noncompact Ricci flows

Liang Cheng, Yongjia Zhang

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


In this note we show that, under certain curvature positivity conditions (the weak 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.

Original languageEnglish (US)
Pages (from-to)519-529
Number of pages11
JournalAnnals of Global Analysis and Geometry
Issue number3
StatePublished - Apr 2022

Bibliographical note

Funding Information:
Liang Cheng’s Research partially supported by Natural Science Foundation of Hubei 2019CFB511.

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature B.V.


  • Expanding breathers
  • Gradient expanding Ricci solitons
  • No breather theorem
  • Noncompact Ricci flows


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