Stephen Shang Yi Liu — Neckpinchhttps://neckpinch.com/authors/stephen-shang-yi-liu/New arXiv papers by Stephen Shang Yi Liu, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT Ricci-DeTurck Flow from Initial Metric with Morrey-type Integrability Conditionhttps://neckpinch.com/papers/2407.06575/arxiv:2407.06575Tue, 09 Jul 2024 00:00:00 GMTMan-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 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.Ricci flowSingularitiesScalar curvatureWeak & singular flowsStability & uniquenessHarmonic maps & DeTurck trick