Smooth compact Ricci flows are characterized weakly solely via metrics and measures by defining super Ricci flows and adding a saturation condition to recover equality.
Topping,Ricci flow: the foundations via optimal transportation, Optimal Transportation, Theory and Applications, LMS lecture notes series,vol
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On weak formulations of (super) Ricci flows
Smooth compact Ricci flows are characterized weakly solely via metrics and measures by defining super Ricci flows and adding a saturation condition to recover equality.