Wedge extendability of CR-meromorphic functions: the minimal case

2000/06/30 by Joel Merker, Egmont Porten
Mathematics · #math.CV #msc:32D20. #msc:32A20 #msc:32D10 #msc:32V10 #msc:32V25 #msc:32V35

paper · pdf

published as Math. Z. 241 (2002), 485-512 · 23 pages, 5 figures, deformations of global analytic discs

arxiv created 2004/04/13 · arxiv updated 2009/11/30

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 L¹-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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