Totally real discs in non-pseudoconvex boundaries

Abstract

LetD be a relatively compact domain in C² with smooth connected boundary ∂D. A compact set K⊂∂D is called removable if any continuous CR function defined on ∂D/K admits a holomorphic extension to D. If D is strictly pseudoconvex, a theorem of B. Jöricke states that any compact K contained in a smooth totally real disc S⊂∂D is removable. In the present article we show that this theorem is true without any assumption on pseudoconvexity.