Extension of positive currents across a CR submanifold (Q1568994)

The author studies the extension of positive currents through obstacles having the CR property. The structure of currents on a CR submanifold is investigated and a support theorem is proved. These results are applied to study the extension of positive currents across real analytic subsets of low dimension and of currents having the boundary extendable across real analytic subsets of CR type. In the particular case of a real analytic Levi-flat submanifold, this study generalizes J.~R.~King and N.~Sibony's results relating to Schwarz's symmetry problem.