### A reflection principle on strongly pseudoconvex domains with generic corners.

Skip to main content (access key 's'),
Skip to navigation (access key 'n'),
Accessibility information (access key '0')

We show that no compact Levi-flat CR manifold of CR codimension one admits a continuous CR function which is nonconstant along leaves of the Levi foliation. We also prove the nonexistence of certain CR functions on a neighborhood of a compact leaf of some Levi-flat CR 3-manifolds, and apply it to showing that some foliated 3-manifolds cannot be embedded as smooth Levi-flat real hypersurfaces in complex surfaces.

Let ${X}_{1}$ and ${X}_{2}$ be two compact strongly pseudoconvex CR manifolds of dimension $2n-1\ge 5$ which bound complex varieties ${V}_{1}$ and ${V}_{2}$ with only isolated normal singularities in ${\u2102}^{N1}$ and ${\u2102}^{N2}$ respectively. Let ${S}_{1}$ and ${S}_{2}$ be the singular sets of ${V}_{1}$ and ${V}_{2}$ respectively and ${S}_{2}$ is nonempty. If $2n-{N}_{2}-1\ge 1$ and the cardinality of ${S}_{1}$ is less than 2 times the cardinality of ${S}_{2}$, then we prove that any non-constant CR morphism from ${X}_{1}$ to ${X}_{2}$ is necessarily a CR biholomorphism. On the other hand, let $X$ be a compact strongly pseudoconvex CR manifold of...

Necessary topological conditions are given for the closed CR embedding of a CR manifold into a Stein manifold or into a complex projective space.