Exposing boundary points of strongly pseudoconvex subvarieties in complex spaces

Deng, F.; Fornæss, J.; Wold, E.

doi:10.1090/proc/13693

Exposing boundary points of strongly pseudoconvex subvarieties in complex spaces
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by F. Deng, J. E. Fornæss and E. F. Wold PDF

Proc. Amer. Math. Soc. 146 (2018), 2473-2487 Request permission

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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