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.
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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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Attribution License 4.0 (CC BY). |
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