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.
@article{hal-00003401,
author = {Merker, Joel and Porten, Egmont},
title = {Wedge extendability of CR-meromorphic functions: the minimal case},
journal = {HAL},
volume = {2002},
number = {0},
year = {2002},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00003401}
}
Merker, Joel; Porten, Egmont. Wedge extendability of CR-meromorphic functions: the minimal case. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00003401/