Hartogs Domains and the Diederich Fornæss Index

2018/09/07 by Muhenned Abdulsahib, Abdulsahib, Muhenned, Phillip S. Harrington +1 · 1 citation
Mathematics · #32U10 #Algebraic Geometry and Number Theory #Analytic and geometric function theory #Commutative Algebra and Its Applications #Complex Variables (math.CV) #FOS: Mathematics #Geometric and Algebraic Topology #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1809.02662

openalex publication_date 2018/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Geometric Analysis on the Diederich-Fornæss Index
• The Diederich-Fornæss index I: for domains of non-trivial index
• The Diederich--Fornæss index II: for domains of trivial index

Cited by

• Sobolev regularity for the ∂--Neumann operator and transverse vector fields

Related

• On the Steinness index
• The Diederich-Fornæss index I: for domains of non-trivial index
• The Diederich--Fornæss index II: for domains of trivial index
• The Diederich-Fornaess Index and Good Vector Fields
• Geometric Analysis on the Diederich-Fornæss Index