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In this article, we consider metrically thin singularities E of the solutions of the tangential Cauchy–Riemann operators on a smoothly embedded Cauchy–Riemann manifold M (CR functions on M\E). Our main result establishes the removability of E within the space of locally integrable functions on M, which are CR on M\E, under the hypothesis that the (dim M-2)-dimensional Hausdorff volume of E is zero and that the CR-orbits of M and of M\E are comparable.

METRICALLY THIN SINGULARITIES OF INTEGRABLE CR FUNCTIONS