A new hypoelliptic operator on almost CR manifolds
Raphaël
Ponge
Source: Rev. Mat. Iberoamericana Volume 27, Number 2
(2011), 393-414.
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 $\mathbb{H}^{5}$.
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Keywords: hypoelliptic operators; $\overline{\partial}_b$-operator; finite type condition; CR structures; contact geometry; pseudodifferential operators
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Permanent link to this document: http://projecteuclid.org/euclid.rmi/1307713032
Zentralblatt MATH identifier: 05936696
Mathematical Reviews number (MathSciNet): MR2848525
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