Corollary 3.6 . [03GZ]

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Corollary 3.6.

Under the same diffeomorphism $\Phi$ as in Proposition 3.4 we have that

(3.32)

|\nabla^{k}_{g_{\mathcal{C}}}(\Phi^{*}\bm{\omega}_{TY}-\bm{\omega}_{\mathcal{C}})|_{g_{\mathcal{C}}}=O(e^{-\underline{\delta}z})

for all $k\geq 0$ , where $\underline{\delta}>0$ is the same constant as in (3.14).