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Transactions of the American Mathematical Society

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Hypoellipticity on Cauchy-Riemann manifolds

Author: Johannes A. Petersen
Journal: Trans. Amer. Math. Soc. 334 (1992), 615-639
MSC: Primary 32F20; Secondary 32F40, 35H05
MathSciNet review: 1113696
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Abstract: Using a recent homotopy formula by Trèves, it is shown that the existence of $ (q + 1)$-dimensional holomorphic supporting manifolds is a sufficient condition for the hypoellipticity on level $ q$ and $ n - q$ of a tangential Cauchy-Riemann complex of $ {\text{CR}}$-dimension $ n$. In the hypersurface case, this result is given microlocally.

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