12 citations · 62 across the 33 of their papers we have counts for
10 papers · 1 filter
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…
Singular positive mass theorem with arbitrary ends
Jianchun Chu, Man-Chun Lee, Jintian Zhu
Motivated by the recent progress on positive mass theorem for asymptotically flat manifolds with arbitrary ends and the Gromov's definition of scalar curvature lower bound for cont…
Rigidity on non-negative intermediate curvature
Jianchun Chu, Kwok-Kun Kwong, Man-Chun Lee
In a recent work of Brendle-Hirsch-Johne, a notion of intermediate curvature was introduced to extend the classical non-existence theorem of positive scalar curvature on torus to p…
Rigidity of Lipschitz map using harmonic map heat flow
Man-Chun Lee, Luen-Fai Tam
Motivated by the Lipschitz rigidity problem in scalar curvature geometry, we prove that if a closed smooth spin manifold admits a distance decreasing continuous map of non-zero deg…
Manifolds with small curvature concentration
Pak-Yeung Chan, Shaochuang Huang, Man-Chun Lee
In this work, we construct distance like functions with integral hessian bound on manifolds with small curvature concentration and use it to construct Ricci flows on manifolds with…
Ricci-Deturck flow from rough metrics and applications
Jianchun Chu, Man-Chun Lee
Motivated by the recent work of Lamm and Simon, in this work we study the short-time existence theory of Ricci-Deturck flow starting from rough metrics which are bi-Lipschitz and h…
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…
Monotonicity of the -Green functions
Pak-Yeung Chan, Jianchun Chu, Man-Chun Lee +1
On a complete -nonparabolic -dimensional manifold with non-negative scalar curvature and vanishing second homology, we establish a sharp monotonicity formula for the proper $…
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…