On the Steinness Index
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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.
KeywordsSteinness index Diederich–Fornæss index Stein neighborhood basis Strong Stein neighborhood basis Worm domains
Mathematics Subject Classification32T20 32T35
The author would like to express his deep gratitude to Professor Kang-Tae Kim for valuable guidance and encouragements, and to Professor N. Shcherbina for fruitful conversations.
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