Lemma 4.4 . [0316]

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Lemma 4.4.

Given any compact set $K\subset M\backslash S$ there is a constant $C_{K}$ such that the sectional curvature of $\tilde{\omega}_{t}$ satisfies

(4.15)

\sup_{K}|\mathrm{Sec}(\tilde{\omega}_{t})|\leqslant C_{K},

for all small $t>0$ .