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

2001/01/20 by Marshall A. Whittlesey, Whittlesey, Marshall A.
Mathematics · #32A40 #32H12 #32V10 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics #math.CV #msc:32A40 #msc:32H12 #msc:32V10

paper · pdf · doi:10.48550/arxiv.math/0101169

32 pages, AMS-TeX

arxiv created 2001/01/20 · openalex publication_date 2001/01/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let S be a generic C-infinity smooth CR manifold in Cⁿ, 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 Cⁿ, 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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