On the noncollapsedness of positively curved Type I ancient Ricci flows

Liang Cheng; Yongjia Zhang

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arXiv · 2102.03508

On the noncollapsedness of positively curved Type I ancient Ricci flows

Liang Cheng·Yongjia Zhang

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Abstract

In this article, 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.

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Liang Cheng, Yongjia Zhang. 2021-02-06. On the noncollapsedness of positively curved Type I ancient Ricci flows. https://arxiv.org/abs/2102.03508

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