Ricci-DeTurck Flow from Initial Metric with Morrey-type Integrability Condition

TL;DR

This paper develops a short-time existence theory for Ricci-DeTurck flow starting from rough metrics with Morrey-type integrability, showing preservation of scalar curvature bounds and applications to singularity removal.

Contribution

It introduces a new existence theory for Ricci-DeTurck flow with Morrey regularity and applies it to scalar curvature rigidity and singularity analysis.

Findings

Preservation of scalar curvature lower bounds under Ricci flow.

Short-time existence for rough initial metrics with Morrey conditions.

Application to removable singularities in scalar curvature rigidity.

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.