Foliations of continuous q-pseudoconcave graphs

Abstract

We show that for $k=0,1$ the graph of a continuous mapping $f:D\to {\mathbb{R}}^k\times {\mathbb{C}}^p$, defined on a domain $D$ in ${\mathbb{C}}^n\times {\mathbb{R}}^k$, is locally foliated by complex $n$-dimensional submanifolds if and only if its complement is $n$-pseudoconvex (in the sense of Rothstein) relatively to $(D\times {\mathbb{R}}^k)\times {\mathbb{C}}^p\subset {\mathbb{C}}^n\times {\mathbb{C}}^k\times {\mathbb{C}}^p$.

20 pages. Comments welcome