Complex submanifolds in real-analytic pseudoconvex hypersurfaces

摘要

A theorem is given that guarantees the existence of nontrivial complex analytic submanifolds in real-analytic pseudoconvex boundaries near real-analytic submanifolds with holomorphic vectorfields on which the Levi form vanishes. Applications to the $\bar{\delta }$-Neumann problem and to the existence of Stein neighborhoods are discussed.