4 papers
Spaces with distributional scalar curvature bounded from below: Optimal regularity and positive mass
Man-Chun Lee, Florian Litzinger, Miles Simon
In this work, we study the positive mass theorem under critical low regularity assumptions using Ricci flow smoothing. We show that asymptotically flat manifolds of regul…
Uniqueness of Ricci flow with scaling invariant estimates
Man-Chun Lee
In this work, we prove uniqueness for complete non-compact Ricci flow with scaling invariant curvature bound. This generalizes the earlier work of Chen-Zhu, Kotschwar and covers mo…
PIC1 pinched manifolds are flat or compact
Alix Deruelle, Man-Chun Lee, Felix Schulze +2
Hamilton's pinching conjecture, that three-dimensional complete non-compact manifolds with pinched Ricci curvature are flat, has recently been resolved using Ricci flow. In this pa…
Ricci-DeTurck Flow from Initial Metric with Morrey-type Integrability Condition
Man-Chun Lee, Stephen Shang Yi Liu
In this work, we study the short-time existence theory of Ricci-DeTurck flow starting from rough metrics which satisfy a Morrey-type integrability condition. Using the rough existe…