The aim of this paper is to present the construction, out of the Kohn-Rossi complex, of a new hypoelliptic operator on almost CR manifolds equipped with a real structure. The operator acts on all -forms, but when restricted to -forms and -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 may fail to be hypoelliptic, as it is shown in the example of the Heisenberg group .
Cite this article
Raphaël Ponge, A new hypoelliptic operator on almost CR manifolds. Rev. Mat. Iberoam. 27 (2011), no. 2, pp. 393–414DOI 10.4171/RMI/641