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Rigidity of positive mass theorem with fast metric decay
Jianchun Chu, Man-Chun Lee, Jingbo Wan
In this work, we consider metrics on Euclidean space with nonnegative scalar curvature and rapid decay at infinity. We show that, in dimensions four and higher, any such metric is…
Quantification of scalar curvature under convergence using smoothing
Man-Chun Lee
A quantitative version of the scalar lower bound under convergence was conjectured by Gromov. More recently, Mazurowski and Yao proved that a refined form of Gromov's conject…
On diameter rigidity for Kähler manifolds with positive holomorphic sectional curvature
Jianchun Chu, Man-Chun Lee, Jintian Zhu
In this paper, we establish some diameter rigidity for Kähler manifolds with positive holomorphic sectional curvature.
Homological -systole in -manifolds and bi-Ricci curvature
Jianchun Chu, Man-Chun Lee, Jintian Zhu
In this paper, we prove an optimal systolic inequality and the corresponding rigidity in the equality case on closed manifolds with positive bi-Ricci curvature, which generalizes t…
On Kähler manifolds with non-negative mixed curvature
Jianchun Chu, Man-Chun Lee, Jintian Zhu
In this work, we investigate compact Kähler manifolds with non-negative or quasi-positive mixed curvature coming from a linear combination of the Ricci and holomorphic sectional cu…
Llarull's theorem on punctured sphere with metric
Jianchun Chu, Man-Chun Lee, Jintian Zhu
The classical Llarull theorem states that a smooth metric on -sphere cannot have scalar curvature no less than and dominate the standard spherical metric at the same ti…
Collapsing immortal Kähler-Ricci flows
Hans-Joachim Hein, Man-Chun Lee, Valentino Tosatti
We consider the Kähler-Ricci flow on compact Kähler manifolds with semiample canonical bundle and intermediate Kodaira dimension, and show that the flow collapses to a canonical me…
Hypercritical deformed Hermitian-Yang-Mills equation revisited
Jianchun Chu, Man-Chun Lee
In this paper, we study the hypercritical deformed Hermitian-Yang-Mills equation on compact Kähler manifolds and resolve two conjectures of Collins-Yau.