7 papers · 1 filter
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…
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…
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…
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…