Lemma 4.11 . [03HM]

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Lemma 4.11.

Let $u$ satisfy $\Delta_{h_{0}}u=0$ and assume $u=u_{\mathfrak{n}}$ , then $u_{\mathfrak{n}}$ is a harmonic function with $u=O(e^{-\delta z})$ for some $\delta>0$ .