Global hypoellipticity of the Kohn-Laplacian $\Box_b$ on pseudoconvex CR manifolds

Details Global hypoellipticity of the Kohn-Laplacian $\Box_b$ on pseudoconvex CR manifolds Global hypoellipticity of the Kohn-Laplacian $\Box_b$ on pseudoconvex CR manifolds

2010-12-29

arxiv.org/abs/1012.5906v1

Mathematics

Complex Variables

Scientific paper

Let $X$ be a complex manifold and $M\subset X$ a compact, smooth, pseudoconvex CR manifold of dimension $2n-1$. (Here $n\ge 3$ or, in case $n=2$, it is made the extra assumption that $\dib_b$ has closed range on functions.) Assume that there exists a strictly CR-plurisubharmonic function in a neighborhood of $M$ in $X$. In this situation, there are here proved \begin{enumerate} \item[(i)] The global existence of $C^\infty$ solutions to the tangential Cauchy-Riemann operator $\dib_b$. \item[(ii)] The global hypoellipticity of the Kohn-Laplacian $\Box_b$, under the additional condition of "weak Property (P)". \end{enumerate}

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