Characterization of Ricci flow solutions via metrics and measures, suggesting new approaches for singular settings.
We present two characterizations of smooth compact Ricci flow solutions solely in terms of metrics and measures (one of them only works under positive scalar curvature along the flow); thus, provide weak formulations that are generalized to the singular setting in a straightforward manner. These characterizations are achieved by weakly formulating super Ricci flows and imposing a saturation condition (solely in terms of metric and measure) to ensure the super Ricci flow inequality is an equality.
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Sajjad Lakzian (2026) studied this question.
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