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A note on plurisubharmonic defining functions in \({\mathbb{C}^{n}}\)

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Abstract

Let \({\Omega\subset\subset\mathbb{C}^{n}}\) , n ≥ 3, be a smoothly bounded domain. Suppose that Ω admits a smooth defining function which is plurisubharmonic on the boundary of Ω. Then a Diederich–Fornæss exponent can be chosen arbitrarily close to 1, and the closure of Ω admits a Stein neighborhood basis.

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Authors and Affiliations

  1. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA

    J. E. Fornæss

  2. Department of Mathematics, University of Vienna, 1090, Vienna, Austria

    A.-K. Herbig

Authors
  1. J. E. Fornæss
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  2. A.-K. Herbig
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Correspondence to A.-K. Herbig.

Additional information

Research of J. E. Fornæss was partially supported by an NSF grant. Research of A.-K. Herbig was supported by FWF grant P19147.

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Fornæss, J.E., Herbig, AK. A note on plurisubharmonic defining functions in \({\mathbb{C}^{n}}\) . Math. Ann. 342, 749–772 (2008). https://doi.org/10.1007/s00208-008-0255-y

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  • DOI: https://doi.org/10.1007/s00208-008-0255-y

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