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Exposing boundary points of strongly pseudoconvex subvarieties in complex spaces


Authors: F. Deng, J. E. Fornæss and E. F. Wold
Journal: Proc. Amer. Math. Soc. 146 (2018), 2473-2487
MSC (2010): Primary 32C15, 32H02
DOI: https://doi.org/10.1090/proc/13693
Published electronically: March 9, 2018
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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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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
Email: fushengd@math.uio.no

J. E. Fornæss
Affiliation: Department for Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway
Email: john.fornass@math.ntnu.no

E. F. Wold
Affiliation: Matematisk Institutt, Universitetet i Oslo, Postboks 1053 Blindern, 0316 Oslo, Norway
Email: erlendfw@math.uio.no

DOI: https://doi.org/10.1090/proc/13693
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
Article copyright: © Copyright 2018 American Mathematical Society

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