Wedge extendability of CR-meromorphic functions: the minimal case

Details Wedge extendability of CR-meromorphic functions: the minimal case Wedge extendability of CR-meromorphic functions: the minimal case

2000-06-23

arxiv.org/abs/math/0006178v2

Math. Z. 241 (2002), 485-512

Mathematics

Complex Variables

23 pages, 5 figures, deformations of global analytic discs

Scientific paper

In this article, we consider metrically thin singularities E of the solutions of the tangential Cauchy-Riemann operators on a C^{2,a}-smooth embedded Cauchy-Riemann generic manifold M (CR functions on M - E) and more generally, we consider holomorphic functions defined in wedgelike domains attached to M - E. Our main result establishes the wedge- and the L^1-removability of E under the hypothesis that the (\dim M-2)-dimensional Hausdorff volume of E is zero and that M and M\backslash E are globally minimal. As an application, we deduce that there exists a wedgelike domain attached to an everywhere locally minimal M to which every CR-meromorphic function on M extends meromorphically.

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