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The Heisenberg group $\mathbb{H}^1$ is known to be conformally equivalent tothe CR sphere $\mathbb{S}^3$ minus a point. We use this fact, together with theknowledge of the tangential Cauchy-Riemann operator on the compact CR manifold$\mathbb{S}^3$, to solve the corresponding operator on $\mathbb{H}^1$.

The tangential Cauchy-Riemann complex on the Heisenberg group Via Conformal Invariance