The Tangential Cauchy-Riemann Complex on The Heisenberg Group via Conformal Invariance
by
Chin-Yu Hsiao
Po Lam Yung
Vol. 8 No. 3 (2013) P.359~P.375
ABSTRACT
The Heisenberg group $\mathbb{H}^1$ is known to be conformally equivalent to the CR sphere $\mathbb{S}^3$ minus a point. We use this fact, together with the knowledge of the tangential Cauchy-Riemann operator on the compact CR manifold $\mathbb{S}^3$, to solve the corresponding operator on $\mathbb{H}^1$.
KEYWORDS
tangential Cauchy-Riemann operator, Heisenberg group, conformal invariance, non-compact CR manifolds, closed range
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 32V20, 32W10
MILESTONES
Received: 2013-01-01
Revised : 2013-05-07
Accepted: 2013-05-08
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