Open Access
May, 2011 A new hypoelliptic operator on almost CR manifolds
Raphaël Ponge
Rev. Mat. Iberoamericana 27(2): 393-414 (May, 2011).


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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Raphaël Ponge . "A new hypoelliptic operator on almost CR manifolds." Rev. Mat. Iberoamericana 27 (2) 393 - 414, May, 2011.


Published: May, 2011
First available in Project Euclid: 10 June 2011

zbMATH: 1262.32042
MathSciNet: MR2848525

Primary: 35H10
Secondary: 32V05 , 32V35 , 32W10 , 35S05 , 53D10

Keywords: $\overline{\partial}_b$-operator , contact geometry , CR structures , finite type condition , hypoelliptic operators , pseudodifferential operators

Rights: Copyright © 2011 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.27 • No. 2 • May, 2011
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