Proposition 2.4 . [007Y]

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Proposition 2.4.

(Almost maximum on top strata II) There is a uniform lower bound for all $|t|\ll 1$ and all $i\in I$ :

\sup_{E_{i}^{0}}u\geq-C,\quad\int_{E_{i}^{0}}u\omega_{\mathcal{X}}|_{X_{t}}^{n}\geq-C^{\prime}.

(3)