12 citations · 62 across the 33 of their papers we have counts for
42 papers
Rigidity of contracting map using harmonic map heat flow
Man-Chun Lee, Jingbo Wan
Motivated by a question of Tsai-Tsui-Wang, we consider the rigidity of map from manifolds with positive Ricci curvature to manifolds with positive sectional curvature. We show that…
Gap Theorem on Riemannian manifolds using Ricci flow
Pak-Yeung Chan, Man-Chun Lee
In this work, we use the Ricci flow approach to study the gap phenomenon of Riemannian manifolds with non-negative curvature and sub-critical scaling invariant curvature decay. The…
Ricci Flow under Kato-type curvature lower bound
Man-Chun Lee
In this work, we extend the existence theory of non-collapsed Ricci flows from point-wise curvature lower bound to Kato-type lower bound. As an application, we prove that compact t…
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…
Kähler tori with almost non-negative scalar curvature
Jianchun Chu, Man-Chun Lee
Motivated by the torus stability problem, in this work we study Kähler metrics with almost non-negative scalar curvature on complex torus. We prove that after passing to a subseque…
Continuous metrics and a conjecture of Schoen
Man-Chun Lee, Luen-Fai Tam
A classical theorem in conformal geometry states that on a manifold with non-positive Yamabe invariant, a smooth metric achieving the invariant must be Einstein. In this work, we e…
Scalar curvature lower bound under integral convergence
Yiqi Huang, Man-Chun Lee
In this work, we consider sequences of metrics which converge to a metric in sense. We show that if the scalar curvature of the sequence is almost non-negative in…
Hypercritical deformed Hermitian-Yang-Mills equation
Jianchun Chu, Man-Chun Lee
In this work, we study the deformed Hermitian-Yang-Mills equation on compact Kähler manifold. We introduce the notions of coerciveness and properness of the -functiona…
Singular metrics with negative scalar curvature
Man-Chuen Cheng, Man-Chun Lee, Luen-Fai Tam
Motivated by the work of Li and Mantoulidis, we study singular metrics which are uniformly Euclidean on a compact manifold () with negative Yamabe invari…
A Nakai-Moishezon type criterion for supercritical deformed Hermitian-Yang-Mills equation
Jianchun Chu, Man-Chun Lee, Ryosuke Takahashi
The deformed Hermitian-Yang-Mills equation is a complex Hessian equation on compact Kähler manifolds that corresponds to the special Lagrangian equation in the context of the Strom…
On the Hölder estimate of Kähler-Ricci flow
Jianchun Chu, Man-Chun Lee
In this work, we study the H\"older regularity of the Kähler- Ricci flow on compact Kähler manifolds with semi-ample canonical line bundle. By adapting the method in the work of…
Conformal tori with almost non-negative scalar curvature
Jianchun Chu, Man-Chun Lee
In this work, we consider sequence of metrics with almost non-negative scalar curvature on torus. We show that if the sequence is uniformly conformal to another sequence of metrics…
Small curvature concentration and Ricci flow smoothing
Pak-Yeung Chan, Eric Chen, Man-Chun Lee
We show that a complete Ricci flow of bounded curvature which begins from a manifold with a Ricci lower bound, local entropy bound, and small local scale-invariant integral curvatu…
convergence and -regularity theorems for entropy and scalar curvature lower bounds
Man-Chun Lee, Aaron Naber, Robin Neumayer
Consider a sequence of Riemannian manifolds with scalar curvatures and entropies bounded below by small constants . The goal of this paper is to und…
Kähler manifolds and mixed curvature
Jianchun Chu, Man-Chun Lee, Luen-Fai Tam
In this work we consider compact Kähler manifolds with non-positive mixed curvature which is a "convex combination" of Ricci curvature and holomorphic sectional curvature. We show…