Abstract
Estimates of the Bergman kernel and the Bergman and Kobayashi metrics on pseudoconvex domains near boundaries with constant Levi ranks are given. As a consequence, a characterization of Levi-flatness in terms of boundary behavior of the Bergman and Kobayashi metrics is obtained.
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Acknowledgements
This paper was part of the author’s Ph.D. thesis at Washington University in St. Louis. The author thanks his thesis advisor Steven Krantz for kind encouragement throughout the years. He also thanks Professors Bo-Yong Chen and Mei-Chi Shaw for stimulating recent discussions on related subjects which help convince him that the results in this paper might still be of current interest.
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Communicated by Steven G. Krantz.
The author was supported in part by NSF grant DMS-1101678.
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Fu, S. Estimates of Invariant Metrics on Pseudoconvex Domains Near Boundaries with Constant Levi Ranks. J Geom Anal 24, 32–46 (2014). https://doi.org/10.1007/s12220-012-9325-1
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DOI: https://doi.org/10.1007/s12220-012-9325-1