The Diederich–Fornæss Exponent and Non-existence of Stein Domains with Levi-Flat Boundaries

Abstract

We study the Diederich–Fornæss exponent and relate it to non-existence of Stein domains with Levi-flat boundaries in complex manifolds. In particular, we prove that if the Diederich–Fornæss exponent of a smooth bounded Stein domain in an $$n$$ -dimensional complex manifold is greater than $$k/n$$ , then it has a boundary point at which the Levi-form has rank greater than or equal to k.