Lemma 2.30 . [041J]

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Lemma 2.30.

Let $\delta<-1$ and $\tau<0$ . If a function $u$ satisfies $\Delta_{g_{\mathbb{C}^{3}}}u=0$ with bound $\left\lVert du\right\rVert_{C^{k+1,\alpha}_{\delta+1,\tau}(\mathbb{C}^{3},\Lambda^{1})}<\infty$ , then $du=0$ .