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On the noncollapsedness of positively curved Type I ancient Ricci flows

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  • Liang Cheng
  • Yongjia Zhang

Abstract

In this paper, we study complete Type I ancient Ricci flows with positive sectional curvature. Our main results are as follows: in the complete and noncompact case, all such ancient solutions must be noncollapsed on all scales; in the closed case, if the dimension is even, then all such ancient solutions must be noncollapsed on all scales. This furthermore gives a complete classification for three‐dimensional noncompact Type I ancient solutions without assuming the noncollapsing condition.

Suggested Citation

  • Liang Cheng & Yongjia Zhang, 2024. "On the noncollapsedness of positively curved Type I ancient Ricci flows," Mathematische Nachrichten, Wiley Blackwell, vol. 297(1), pages 102-109, January.
    • Handle: RePEc:bla:mathna:v:297:y:2024:i:1:p:102-109
    DOI: 10.1002/mana.202200335
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