On the noncollapsedness of positively curved Type I ancient Ricci flows

Liang Cheng and Yongjia Zhang

Mathematische Nachrichten, 2024, vol. 297, issue 1, 102-109

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.

Date: 2024
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https://doi.org/10.1002/mana.202200335

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