On the Steinness Index

Jihun Yum

doi:10.1007/s12220-018-0053-z

On the Steinness Index

Jihun Yum^*

^*Corresponding author for this work

Department of Mathematics Education

Pohang University of Science and Technology

Research output: Contribution to journal › Journal article › peer-review

6 Scopus citations

Abstract

We introduce the concept of Steinness index related to the Stein neighborhood basis. We then show several results: (1) The existence of Steinness index is equivalent to that of strong Stein neighborhood basis. (2) On the Diederich–Fornæss worm domains in particular, we present an explicit formula relating the Steinness index to the well-known Diederich–Fornæss index. (3) The Steinness index is 1 if a smoothly bounded pseudoconvex domain admits finitely many boundary points of infinite type.

Original language	English
Pages (from-to)	1583-1607
Number of pages	25
Journal	Journal of Geometric Analysis
Volume	29
Issue number	2
DOIs	https://doi.org/10.1007/s12220-018-0053-z
State	Published - 2019.04.15

Keywords

Diederich–Fornæss index
Stein neighborhood basis
Steinness index
Strong Stein neighborhood basis
Worm domains

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10.1007/s12220-018-0053-z

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title = "On the Steinness Index",

abstract = "We introduce the concept of Steinness index related to the Stein neighborhood basis. We then show several results: (1) The existence of Steinness index is equivalent to that of strong Stein neighborhood basis. (2) On the Diederich–Forn{\ae}ss worm domains in particular, we present an explicit formula relating the Steinness index to the well-known Diederich–Forn{\ae}ss index. (3) The Steinness index is 1 if a smoothly bounded pseudoconvex domain admits finitely many boundary points of infinite type.",

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AB - We introduce the concept of Steinness index related to the Stein neighborhood basis. We then show several results: (1) The existence of Steinness index is equivalent to that of strong Stein neighborhood basis. (2) On the Diederich–Fornæss worm domains in particular, we present an explicit formula relating the Steinness index to the well-known Diederich–Fornæss index. (3) The Steinness index is 1 if a smoothly bounded pseudoconvex domain admits finitely many boundary points of infinite type.

KW - Diederich–Fornæss index

KW - Stein neighborhood basis

KW - Steinness index

KW - Strong Stein neighborhood basis

KW - Worm domains

UR - https://www.scopus.com/pages/publications/85048832029

U2 - 10.1007/s12220-018-0053-z

DO - 10.1007/s12220-018-0053-z

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AN - SCOPUS:85048832029

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VL - 29

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EP - 1607

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 2

ER -

On the Steinness Index

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Keywords

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