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On the Steinness Index

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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.

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Acknowledgements

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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Authors and Affiliations

  1. Department of Mathematics, Pohang University of Science and Technology, Pohang, 790-784, Republic of Korea

    Jihun Yum

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  1. Jihun Yum
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Correspondence to Jihun Yum.

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This research was supported by the SRC-GAIA (NRF-2011-0030044) through the National Research Foundation of Korea (NRF) funded by the Ministry of Education.

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Yum, J. On the Steinness Index. J Geom Anal 29, 1583–1607 (2019). https://doi.org/10.1007/s12220-018-0053-z

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  • DOI: https://doi.org/10.1007/s12220-018-0053-z

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