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arXiv · 1607.02755

Exposing boundary points of strongly pseudoconvex subvarieties in complex spaces

Fusheng Deng·John Erik Fornaess·Erlend Fornaess Wold
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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 $\mathbb C^n$. For a bounded strongly pseudoconvex domain in $\mathbb C^n$ 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 $C^1$-norm and maps the boundary point to a strongly convex boundary point.

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Fusheng Deng, John Erik Fornaess, Erlend Fornaess Wold. 2016-07-10. Exposing boundary points of strongly pseudoconvex subvarieties in complex spaces. https://arxiv.org/abs/1607.02755

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