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arXiv · 2002.06586

Bounded Ricci Curvature and Positive Scalar Curvature under Singular Ricci de Turck Flow

Klaus Kroencke·Tobias Marxen·Boris Vertman
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Abstract

In this paper we consider a Ricci de Turck flow of spaces with isolated conical singularities, which preserves the conical structure along the flow. We establish that a given initial regularity of Ricci curvature is preserved along the flow. Moreover under additional assumptions, positivity of scalar curvature is preserved under such a flow, mirroring the standard property of Ricci flow on compact manifolds. The analytic difficulty is the a priori low regularity of scalar curvature at the conical tip along the flow, so that the maximum principle does not apply. We view this work as a first step toward studying positivity of the curvature operator along the singular Ricci flow.

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Klaus Kroencke, Tobias Marxen, Boris Vertman. 2020-02-16. Bounded Ricci Curvature and Positive Scalar Curvature under Singular Ricci de Turck Flow. https://doi.org/10.2140/pjm.2023.324.295

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