Joe J. Perez
A Transversal Fredholm Property for the $\bar\partial$--Neumann Problem on $G$--Bundles
Preprint series: ESI preprints

MSC:

32F20 $\overline\partial$- and $\overline\partial_b$-Neumann problems, See also {35N15}

35N15 $\overline\partial$-Neumann problem and generalizations; formal complexes, See also {32F20 and 58G05}

35H05 Hypoelliptic equations and systems, See also {58Gxx}

Abstract: Let $M$ be a strongly pseudoconvex complex manifold which is also the
total space of a principal $G$-bundle with compact base $M/G$. Assume
also that $G$ acts on $M$ by holomorphic transformations. For such $M$, we
provide a simple condition on forms $\alpha$ sufficient for the regular
solvability of $\square u=\alpha$ and other problems related to the
$\bar\partial$-Neumann problem on $M$. Similar properties are shared by $\square_b$.