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The Ricci–DeTurck
flow from an initial metric with a Morrey-type integrability
condition
Man-Chun Lee and Stephen Shang Yi Liu |
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Vol. 340 (2026), No. 2, 375–397
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Abstract |
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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. |
Keywords
Ricci flow, Ricci–DeTurck flow, scalar curvature rigidity,
singular metrics
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Mathematical Subject Classification
Primary: 53E20
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Milestones
Received: 13 July 2024
Revised: 19 September 2025
Accepted: 6 October 2025
Published: 26 November 2025
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Authors |
| Man-Chun Lee | |
| Department of Mathematics Chinese University of Hong Kong Hong Kong |
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| Stephen Shang Yi Liu | |
| Department of Mathematics Hong Kong University of Science and Technology Hong Kong |
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| © 2026 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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