The Ricci–DeTurck flow from an initial metric with a Morrey-type integrability condition

Rare & Special e-Zone (The Hong Kong University of Science and Technology) 2026

View at publisher
Authors: Man-Chun Lee, Stephen Shang Yi Liu
DOI: 10.2140/pjm.2026.340.375
Cited by: 1
References: 17

Abstract

We study the short-time existence theory of Ricci–DeTurck flow starting from rough metrics that 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 Ricci flow smoothing to study the removable singularity related to scalar curvature. Our result supplements those of Jiang, Sheng and Zhang.

Fields of Study & Subjects

Geometric Analysis and Curvature Flows Geometry and complex manifolds Nonlinear Partial Differential Equations

Publication details

Journal / source
Rare & Special e-Zone (The Hong Kong University of Science and Technology)
Publisher
Mathematical Sciences Publishers
Volume
340
Issue
2
Pages
375-397
Publication date
1 January 2026
Language
EN