A General Version of the Hartogs Extension Theorem for Separately Holomorphic Mappings between Complex Analytic Spaces

Using recent development in Poletsky theory of discs, we prove the following result: Let X, Y be two complex manifolds, let Z be a complex analytic space which possesses the Hartogs extension property, let A (resp. B) be a non locally pluripolar subset of X (resp. Y ). We show that every separately holomorphic mapping f : W := (A × Y ) ∪ (X × B) −→ Z extends to a holomorphic mapping f̂ on Ŵ := {(z, w) ∈ X × Y : ω̃(z, A, X) + ω̃(w, B, Y ) < 1} such that f̂ = f on W ∩ Ŵ , where ω̃(·, A, X) (resp. ω̃(·, B, Y )) is the plurisubharmonic measure of A (resp. B) relative to X (resp. Y ). Generalizations of this result for an N -fold cross are also given.