Revista Matemática Iberoamericana


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Volume 27, Issue 2, 2011, pp. 393–414
DOI: 10.4171/RMI/641

Published online: 2011-08-31

A new hypoelliptic operator on almost CR manifolds

Raphaël Ponge[1]

(1) Seoul National University, South Korea

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 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 $\mathbb{H}^{5}$.

Keywords: Hypoelliptic operators, $\overline{\partial}_b$-operator, finite type condition, CR structures, contact geometry, pseudodifferential operators

Ponge Raphaël: A new hypoelliptic operator on almost CR manifolds. Rev. Mat. Iberoamericana 27 (2011), 393-414. doi: 10.4171/RMI/641