Ricci-DeTurck Flow from Initial Metric with Morrey-type Integrability Condition
Differential Geometry
2025-11-26 v3
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.
Cite
@article{arxiv.2407.06575,
title = {Ricci-DeTurck Flow from Initial Metric with Morrey-type Integrability Condition},
author = {Man-Chun Lee and Stephen Shang Yi Liu},
journal= {arXiv preprint arXiv:2407.06575},
year = {2025}
}
Comments
23 pages; abstract updated; references updated and revised according to reviewer comments. To appear, Pacific Journal of Mathematics