Abstract
We propose the concept of Diederich–Fornæss and Steinness indices on compact pseudoconvex CR manifolds of hypersurface type in terms of the D’Angelo 1-form. When the CR manifold bounds a domain in a complex manifold, under certain additional non-degeneracy conditions, those indices are shown to coincide with the original Diederich–Fornæss and Steinness indices of the domain, and CR invariance of the original indices follows.
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Acknowledgements
The authors would like to thank Kengo Hirachi for suggesting Remark 2.3 and the referees for their careful reading and suggestions to improve the presentation of this article.
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Masanori Adachi is partially supported by a JSPS KAKENHI Grant Number JP18K13422.
Jihun Yum is supported by the Institute for Basic Science (IBS-R032-D1).
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Adachi, M., Yum, J. Diederich–Fornæss and Steinness Indices for Abstract CR Manifolds. J Geom Anal 31, 8385–8413 (2021). https://doi.org/10.1007/s12220-020-00598-6
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DOI: https://doi.org/10.1007/s12220-020-00598-6