Pointwise lower scalar curvature bounds for $$C^0$$ metrics via regularizing Ricci flow

By Paula Burkhardt-Guim. Geometric and Functional Analysis, 2019

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In this paper we propose a class of local definitions of weak lower scalar curvature bounds that is well defined for $$C^0$$ metrics. We show the following: that our definitions are stable under greater-than-second-order perturbation of the metric, that there exists a reasonable notion of a Ricci flow starting from $$C^0$$ initial data which is smooth for positive times, and that the weak lower scalar curvature bounds are preserved under evolution by the Ricci flow from $$C^0$$ initial data.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/6b4fb56c46514dc73df122a74c441a42ccc377bd