A new hypoelliptic operator on almost CR manifolds

  • Raphaël Ponge

    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 QLQ_L on almost CR manifolds equipped with a real structure. The operator acts on all (p,q)(p,q)-forms, but when restricted to (p,0)(p,0)-forms and (p,n)(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 QLQ_L may fail to be hypoelliptic, as it is shown in the example of the Heisenberg group H5\mathbb{H}^{5}.

Cite this article

Raphaël Ponge, A new hypoelliptic operator on almost CR manifolds. Rev. Mat. Iberoam. 27 (2011), no. 2, pp. 393–414

DOI 10.4171/RMI/641