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December 2019 Hartogs domains and the Diederich–Fornæss index
Muhenned Abdulsahib, Phillip S. Harrington
Illinois J. Math. 63(4): 485-511 (December 2019). DOI: 10.1215/00192082-7937302

Abstract

We study a geometric property of the boundary on Hartogs domains which can be used to find upper and lower bounds for the Diederich–Fornæ ss index. Using this property, we are able to show that under some reasonable hypotheses on the set of weakly pseudoconvex points, the Diederich–Fornæss index for a Hartogs domain is equal to one if and only if the domain admits a family of good vector fields in the sense of Boas and Straube. We also study the analogous problem for a Stein neighborhood basis and show that, under the same hypotheses, if the Diederich–Fornæss index for a Hartogs domain is equal to one, then the domain admits a Stein neighborhood basis.

Citation

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Muhenned Abdulsahib. Phillip S. Harrington. "Hartogs domains and the Diederich–Fornæss index." Illinois J. Math. 63 (4) 485 - 511, December 2019. https://doi.org/10.1215/00192082-7937302

Information

Received: 28 September 2018; Revised: 1 August 2019; Published: December 2019
First available in Project Euclid: 19 November 2019

zbMATH: 07136344
MathSciNet: MR4032812
Digital Object Identifier: 10.1215/00192082-7937302

Subjects:
Primary: 32U10
Secondary: 32T27

Rights: Copyright © 2019 University of Illinois at Urbana-Champaign

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Vol.63 • No. 4 • December 2019
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