Foliation by graphs of CR mappings and a nonlinear Riemann-Hilbert problem for smoothly bounded domains
Complex Variables
2007-05-23 v1
Abstract
Let S be a generic C-infinity smooth CR manifold in C^n, n > 1, and let M be a generic C-infinity CR submanifold of S X C^m. 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 C^n, n > 1. 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.
Cite
@article{arxiv.math/0101169,
title = {Foliation by graphs of CR mappings and a nonlinear Riemann-Hilbert problem for smoothly bounded domains},
author = {Marshall A. Whittlesey},
journal= {arXiv preprint arXiv:math/0101169},
year = {2007}
}
Comments
32 pages, AMS-TeX