4 papers
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…
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…