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.References
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Additional Information
- F. Deng
- Affiliation: Matematisk Institutt, Universitetet i Oslo, Postboks 1053 Blindern, 0316 Oslo, Norway – and – School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China
- MR Author ID: 838477
- Email: fushengd@math.uio.no
- J. E. Fornæss
- Affiliation: Department for Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway
- MR Author ID: 68145
- Email: john.fornass@math.ntnu.no
- E. F. Wold
- Affiliation: Matematisk Institutt, Universitetet i Oslo, Postboks 1053 Blindern, 0316 Oslo, Norway
- MR Author ID: 757618
- Email: erlendfw@math.uio.no
- Received by editor(s): July 10, 2016
- Received by editor(s) in revised form: February 2, 2017, and February 7, 2017
- Published electronically: March 9, 2018
- Communicated by: Franc Forstneric
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 2473-2487
- MSC (2010): Primary 32C15, 32H02
- DOI: https://doi.org/10.1090/proc/13693
- MathSciNet review: 3778150