Abstract
The aim of this paper is to show that it makes sense to write the continuity equation on a metric measure space \((X,\mathsf{d},{\mathfrak {m}})\) and that absolutely continuous curves \((\mu _t)\) w.r.t. the distance \(W_2\) can be completely characterized as solutions of the continuity equation itself, provided we impose the condition \(\mu _t\le C{\mathfrak {m}}\) for every \(t\) and some \(C>0\).
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References
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Communicated by L. Ambrosio.
