Exposing boundary points of strongly pseudoconvex subvarieties in complex spaces

Abstract

We prove that all locally exposable points in a Stein compact in a complex space can be exposed along a given curve to a given real hypersurface. Moreover, the exposing map for a boundary point can be sufficiently close to the identity map outside any fixed neighborhood of the point. We also prove a parametric version of this result for bounded strongly pseudoconvex domains in Cn. For a bounded strongly pseudoconvex domain in Cn and a given boundary point of it, we prove that there is a global coordinate change on the closure of the domain which is arbitrarily close to the identity map with respect to the C1 -norm and maps the boundary point to a strongly convex boundary point.