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Wedge extendability of CR-meromorphic functions: the minimal case

Joel Merker·Egmont Porten
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Abstract

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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Joel Merker, Egmont Porten. 2004-04-13. Wedge extendability of CR-meromorphic functions: the minimal case. https://arxiv.org/abs/math/0006178

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