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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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