Prolongement de courants positifsà travers une sous-variété CR

AbstractIn this paper, we prove an extension theorem through a Cauchy–Riemann submanifold of Cn, for positive currents. In the particular case of a real analytic Levi-flat submanifold, we complete this study by generalizing J.R. King and N. Sibony's results relating to Schwarz's symmetry problem. We were induced to describe the structure of locally flat currents with support in CR submanifolds. Furthermore, we apply our result to study extension of positive currents across real analytic subsets.RésuméIn this paper, we prove an extension theorem through a Cauchy–Riemann submanifold of Cn, for positive currents. In the particular case of a real analytic Levi-flat submanifold, we complete this study by generalizing J.R. King and N. Sibony's results relating to Schwarz's symmetry problem. We were induced to describe the structure of locally flat currents with support in CR submanifolds. Furthermore, we apply our result to study extension of positive currents across real analytic subsets