Lemma 3.18 . [0435]

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Lemma 3.18.

For $\varrho\gtrsim A^{1/2}$ ,

|\nabla^{2}_{g_{a}}G_{a}-\nabla^{2}_{g_{a}}\bar{G}_{a}|_{g_{a}}\leq CA^{-2}e^{-2\pi A^{-1/2}\varrho}.