12 citations · 62 across the 33 of their papers we have counts for
9 papers · 1 filter
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…