setting to that considered in [@KotschwarWangConical], and can be resolved by the same argument (the application of appropriate Carleman inequalities) given in that reference. We discuss the application of these results to the first assertion of Theorem \[thm:kaehlerity\] in Section 3, and prove the second assertion, concerning the extension of the Kähler structure to the entire manifold, with a short synthetic argument in Section 4.

Backward propagation of Kählerity under the Ricci flow
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In this section, we will assume that $g_0$ is a Kähler metric on $M$ with complex structure $J_0$ and that $g = g(\tau)$ is a smooth family of metrics satisfying the *backward Ricci flow* $$\label{eq:brf}
 {{\frac{\partial }{\partial\tau}}}g = 2{\operatorname{Rc}}(g)$$ on $M\times [0, T]$ with $g(0) = g_0$. We do not assume here that $g(\tau)$ is self-similar or that $(M, g(\tau))$ is complete.

Our aim is to set up a framework to determine when the Kählerity of the metric $g_0$ is transferred to $g(\tau)$ for $\tau > 0$. As we have noted above, we cannot simply reduce the problem of the the propagation of the Kähler structure to that of the uniqueness of *solutions* to (that is, to the problem of backward uniqueness of solutions to the 