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

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

2001-01-20

arxiv.org/abs/math/0101169v1

Mathematics

Complex Variables

32 pages, AMS-TeX

Scientific paper

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.

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