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A new hypoelliptic operator on almost CR manifolds. (English) Zbl 1262.32042

Summary: The aim of this paper is to present the construction, out of the Kohn-Rossi complex, of a new hypoelliptic operator \(Q_L\) on almost CR manifolds equipped with a real structure. The operator acts on all \((p,q)\)-forms, but when restricted to \((p,0)\)-forms and \((p,n)\)-forms it is a sum of squares up to sign factor and lower order terms. Therefore, only a finite type condition is needed to have hypoellipticity on those forms. However, outside these forms \(Q_L\) may fail to be hypoelliptic, as it is shown in the example of the Heisenberg group \(\mathbb{H}^{5}\).

MSC:

32V99 CR manifolds
32W50 Other partial differential equations of complex analysis in several variables
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