Ricci-DeTurck Flow from Initial Metric with Morrey-type Integrability Condition
arXiv:2407.06575 · doi:10.2140/pjm.2026.340.375
Abstract
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 existence theory, we show the preservation and improvement of distributional scalar curvature lower bounds provided the singular set for such metrics is not too large. As an application, we use the Ricci flow smoothing to study the removable singularity for scalar curvature rigidity in the compact case under Morrey regularity conditions. Our result supplements those of Jiang-Sheng-Zhang.
23 pages; abstract updated; references updated and revised according to reviewer comments. To appear, Pacific Journal of Mathematics