Metrically thin singularities of integrable CR functions

Joel Merker (1) , Egmont Porten (2)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités
2 Max-Planck-Gesellschaft

In this article, we consider metrically thin singularities A of the tangential Cauchy-Riemann operator on smoothly embedded Cauchy-Riemann manifolds M. The main result states removability within the space of locally integrable functions on M under the hypothesis that the (dim M-2)-dimensional Hausdorff volume of A is zero and that the CR-orbits of M and M-A are comparable.

Mots clés: Integrable CR functions; removable singularities for the tangential Cauchy-Riemann operator; analytic discs

Domaines: Géométrie différentielle [math.DG]

Joel Merker, Egmont Porten. Metrically thin singularities of integrable CR functions. International Journal of Mathematics, 2000, 11, pp.857-872. ⟨hal-00003375⟩