Compactness theory of the space of Super Ricci flows

Bamler, Richard

doi:10.1007/s00222-023-01196-3

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The Nash Entropy and Noncollapsing1

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2023

2024

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Cited by 13 publications

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“…Remark Though Bamler [2] proved the above result for Ricci flows on closed manifolds, yet one may check the proof of Theorem 6.1 in [2] and easily verify its validity for Ricci flows with bounded geometry on each time‐slice; one may need to apply Theorem 4.4 of [21] in this verification. Indeed, Bamler's recent preprint [3] also pointed out the fact that his theory in [2] can be generalized to this more general case. Fortunately, all the Ricci flows we work with in this paper satisfy this condition.…”

Section: The Nash Entropy and Noncollapsingmentioning

confidence: 99%

On the noncollapsedness of positively curved Type I ancient Ricci flows

Cheng

2023

Mathematische Nachrichten

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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.

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