Revista Matemática Iberoamericana

A new hypoelliptic operator on almost CR manifolds

Raphaël Ponge

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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

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

First available in Project Euclid: 10 June 2011

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Zentralblatt MATH identifier

Primary: 35H10: Hypoelliptic equations
Secondary: 32W10: $\overline\partial_b$ and $\overline\partial_b$-Neumann operators 32V35: Finite type conditions on CR manifolds 32V05: CR structures, CR operators, and generalizations 53D10: Contact manifolds, general 35S05: Pseudodifferential operators

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), no. 2, 393--414.

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