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As a consequence, we obtain the following geometric Hardy inequality in a half-space on the Heisenberg group with a sharp constant\n  \\begin{equation*}\n  \\int_{\\mathbb{H}^+} |\\nabla_{H}u|^p d\\xi \\geq \\left(\\frac{p-1}{p}\\right)^p \\int_{\\mathbb{H}^+} \\frac{\\mathcal{W}(\\xi)^p}{dist(\\xi,\\partial \\mathbb{H}^+)^p} |u|^p d\\xi, \\,\\, p>1,\n  \\end{equation*}\n  which solves the conjecture in the paper \\cite{Larson}. 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