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Parabolic Schwarz lemma

You are computing $\Delta_g \operatorname{tr}_g(f^{\ast}h) = g^{i \bar{j}} \partial_i \partial_{\bar{j}} (g^{k\bar{\ell}} h_{\gamma \bar{\delta}} f_k^{\gamma} \bar{f_{\ell}^{\delta}})$ in normal ...
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