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Fix a point $p \\in \\hat{X}$ and take a global contact form $\\hat{\\theta}$ so that $\\hat{\\theta}$ is asymptotically flat near $p$. Then $(\\hat{X}, T^{1,0} \\hat{X}, \\hat{\\theta})$ is a pseudohermitian $3$-manifold. Let $G_p \\in C^{\\infty} (\\hat{X} \\setminus \\{p\\})$, $G_p > 0$, with $G_p(x) \\sim \\vartheta(x,p)^{-2}$ near $p$, where $\\vartheta(x,y)$ denotes the natural pseudohermitian distance on $\\hat{X}$. 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Fix a point $p \\in \\hat{X}$ and take a global contact form $\\hat{\\theta}$ so that $\\hat{\\theta}$ is asymptotically flat near $p$. Then $(\\hat{X}, T^{1,0} \\hat{X}, \\hat{\\theta})$ is a pseudohermitian $3$-manifold. Let $G_p \\in C^{\\infty} (\\hat{X} \\setminus \\{p\\})$, $G_p > 0$, with $G_p(x) \\sim \\vartheta(x,p)^{-2}$ near $p$, where $\\vartheta(x,y)$ denotes the natural pseudohermitian distance on $\\hat{X}$. 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