Proposition 4.16 . [045F]

Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.

Complete original source context · Original author HTML

Proposition 4.16.

(leading order asymptote near $S$ ) Via the local diffeomorphism $\Psi$ , on the chart $\{r\lesssim A^{1/4}\}$ ,

\begin{cases}|\Psi^{*}(w^{p\bar{q}}d\eta_{p}\otimes d\bar{\eta}_{q})-\frac{1}{2\sqrt{\mu^{2}+|\xi_{1}|^{2}}}d\xi_{1}\otimes d\bar{\xi}_{1}|_{g_{a}}\leq CA^{-3/4}\max(1,\log(A^{-1/4}\varrho),\\ |\Psi^{*}v-\frac{1}{2\sqrt{\mu^{2}+|\xi_{1}|^{2}}}|\leq CA^{1/4}\max(1,\log(A^{-1/4}\varrho),\end{cases}