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Manifolds with PIC1 pinched curvature
Man-Chun Lee, Peter M. Topping
Recently it has been proved (Lee-Topping 2022, Deruelle-Schulze-Simon 2022, Lott 2019) that three-dimensional complete manifolds with non-negatively pinched Ricci curvature must be…
Three-manifolds with non-negatively pinched Ricci curvature
Man-Chun Lee, Peter M. Topping
We show that every complete non-compact three-manifold with non-negatively pinched Ricci curvature admits a complete Ricci flow solution for all positive time, with scale-invariant…
Metric limits of manifolds with positive scalar curvature
Man-Chun Lee, Peter M. Topping
We show that any Riemannian metric conformal to the round metric on , for , arises as a limit of a sequence of Riemannian metrics of positive scalar curvature on $S^n…
Time zero regularity of Ricci flow
Man-Chun Lee, Peter M. Topping
We consider the problem of when a smooth Ricci flow, for positive time, that attains smooth initial data in a weak sense must be smooth down to the initial time. We obtain curvatur…