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arXiv · 1809.02662

Hartogs Domains and the Diederich Fornæss Index

Muhenned Abdulsahib·Phillip S. Harrington
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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-Fornæss Index. Using this, 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.

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BibTeXRIS

Muhenned Abdulsahib, Phillip S. Harrington. 2019-06-10. Hartogs Domains and the Diederich Fornæss Index. https://arxiv.org/abs/1809.02662

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