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 $>k/n$, then it has a boundary point at which the Levi-form has rank $\ge k$.

9 pages

References in corpus (1)

• A global estimate for the Diederich--Fornaess index of weakly pseudoconvex domains

Cited by in corpus (1)

• Curvature restrictions for Levi-flat real hypersurfaces in complex projective planes