Exposing boundary points of strongly pseudoconvex subvarieties in complex spaces
Complex Variables
2016-07-12 v1
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 . For a bounded strongly pseudoconvex domain in 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 -norm and maps the boundary point to a strongly convex boundary point.
Cite
@article{arxiv.1607.02755,
title = {Exposing boundary points of strongly pseudoconvex subvarieties in complex spaces},
author = {Fusheng Deng and John Erik Fornaess and Erlend Fornaess Wold},
journal= {arXiv preprint arXiv:1607.02755},
year = {2016}
}