
SIGMA 16 (2020), 128, 10 pages arXiv:2007.14967
https://doi.org/10.3842/SIGMA.2020.128
Contribution to the Special Issue on Scalar and Ricci Curvature in honor of Misha Gromov on his 75th Birthday
Defining Pointwise Lower Scalar Curvature Bounds for $C^0$ Metrics with Regularization by Ricci Flow
Paula BurkhardtGuim
Department of Mathematics, University of California, Berkeley, USA
Received July 30, 2020, in final form November 19, 2020; Published online December 04, 2020
Abstract
We survey some recent work using Ricci flow to create a class of local definitions of weak lower scalar curvature bounds that is well defined for $C^0$ metrics. We discuss several properties of these definitions and explain some applications of this approach to questions regarding uniform convergence of metrics with scalar curvature bounded below. Finally, we consider the relationship between this approach and some other generalized notions of lower scalar curvature bounds.
Key words: Ricci flow; scalar curvature; synthetic lower curvature bounds.
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