Abstract for paper #6

Foliation by graphs of CR mappings and a nonlinear Riemann-Hilbert problem for smoothly bounded domains.

Abstract

Let S be a generic C-infinity smooth CR manifold in Cⁿ, n > 2, and let M be a generic C-infinity CR submanifold of S× C^m, m> 1. We prescribe conditions on M so that it is the disjoint union of graphs of CR maps f:S-->C^m. We also consider the special case where S is the boundary of a bounded, smoothly bounded open set D in Cⁿ, n > 2. In this case we obtain conditions which guarantee that such an f above extends to be analytic on D. This provides a solution to a particular nonlinear Riemann-Hilbert boundary value problem for analytic functions.