## Revista Matemática Iberoamericana

### A new hypoelliptic operator on almost CR manifolds

Raphaël Ponge

#### Abstract

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

#### Article information

Source
Rev. Mat. Iberoamericana, Volume 27, Number 2 (2011), 393-414.

Dates
First available in Project Euclid: 10 June 2011

https://projecteuclid.org/euclid.rmi/1307713032

Mathematical Reviews number (MathSciNet)
MR2848525

Zentralblatt MATH identifier
1262.32042

#### Citation

Ponge, Raphaël. A new hypoelliptic operator on almost CR manifolds. Rev. Mat. Iberoamericana 27 (2011), no. 2, 393--414. https://projecteuclid.org/euclid.rmi/1307713032

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